MOORE  AND  MINER  SERIES 

PRACTICAL  BUSINESS 
ARITHMETIC 


BY 
JOHN  H.  MOORE 

AND 

GEORGE  W.  MINER 


REVISED  BY 

GEORGE  W.  MINER 


GINN  AND  COMPANY 

BOSTON  •  NEW  YORK  •  CHICAGO  •  LONDON 


yt 


<^\5 


COPYRIGHT,  1906,  BY 
JOHN  H.  MOORE  and  GEORGE  W.  MINER 


COPYRIGHT,  1915,  BY 
GEORGE  W.  MINER 


ALL   RIGHTS   RESERVED 
515.1 

eOUCATION  DEPT 


gfte   gtftenaeum   Bttea 

GINN  AND  COMPANY  •  PRO- 
PRIETORS •  BOSTON  •  U.S.A. 


PREFACE 

The  revised  edition  of  the  Practical  Business  Arithmetic  retains 
those  features  of  the  first  edition  that  are  so  highly  commended 
by  teachers ;  namely,  the  development  of  each  topic  in  such  a 
manner  as  to  make  it  practical  and  helpful  to  the  student ;  the 
presentation  of  each  subject  in  a  logical  order;  the  selection  of 
problems  that  appeal  to  the  needs  and  the  interest  of  the  student, 
and  of  the  community  as  well ;  the  omission  of  complex  and 
useless  problems ;  a  plan  of  grading  and  grouping  problems  which 
aids  the  student  in  acquiring  facility  and  advancing  his  educational 
equipment;  the  elimination  of  subjects  which  have  little  or  no 
connection  with  business  interests  and  which  have  slight  practical 
value  ;  the  inclusion  of  an  amount  of  work  that  will  contribute 
to  real  efficiency ;  the  development  of  subjects  inductively  and 
the  omission  of  set  rules ;  the  unusual  amount  of  oral  work  in 
the  different  chapters. 

The  revised  edition  introduces  the  parcel  post,  the  income  tax, 
the  postal  savings  bank,  the  computation  of  loss  and  gain  on  the 
selling  price,  tests  on  a  time  limit,  a  tariff  schedule  in  accord- 
ance with  the  most  recent  legislative  enactments,  additional  work 
on  graphs,  statistical  matter  based  on  the  latest  census,  and  an 
appendix  on  the  varied  uses  of  the   adding  machine. 

In  the  first  edition  the  authors  acknowledged  their  indebtedness 
to  Dr.  David  Eugene  Smith,  Professor  of  Mathematics,  Teachers 
College,  Columbia  University,  New  York,  who  read  the  complete 
manuscript  and  much  of  the  proof,  and  kindly  made  numerous 
suggestions  for  the  betterment  of  the  book ;  to  Mr.  George  M. 
Clough  of  Somerville,  Massachusetts,  for  the  larger  part  of  the 
material  in  the  chapter  on  life  insurance ;  to  Mr.  George  Abbot 

iii 

541601 


iv  PRACTICAL  BUSINESS  ARITHMETIC 

of  Brown  Bros.  &  Co.,  Boston,  and  to  Mr.  H.  T.  Smith,  Assist- 
ant Cashier  of  the  Shawmut  National  Bank,  Boston,  for  valuable 
assistance  on  the  chapters  on  interest  and  banking. 

In  the  present  edition  the  author  is  indebted  to  Mr.  Wm.  B. 
Medlicott,  Lecturer  on  Property  Insurance  at  Harvard  University, 
for  his  work  on  the  chapter  on  property  insurance ;  to  Mr. 
Montgomery  Rollins  of  Boston,  author  of  "  Money  and  Invest- 
ments," and  to  Mr.  Harold  T.  Sibley  of  Chicago,  for  suggestions 
on  the  chapter  on  stocks  and  bonds  ;  to  Mr.  Alexander  H.  Sproul 
of  the  State  Normal  School,  Salem,  Massachusetts,  and  to  Mr. 
C.  D.  McGregor  of  Des  Moines,  Iowa,  for  reading  the  manuscript 
as  a  whole,  and  for  their  cooperation  in  revising  the  text. 


(^ 


^21 


CONTENTS 


FUNDAMENTAL   PROCESSES 

CHAPTER  PAGE 

I.    Introduction 1 

II.     Notation  and  Numeration 2 

III.  United  States  Money 8 

IV.  Addition •        •        •        .10 

V.     Subtraction 31 

VI.     Multiplication 50 

VII.     Division 66 

VIII.     Average 85 

IX.    Checking  Results 87 

FRACTIONS 

X.     Decimal  Fractions 91 

XI.     Factors,  Divisors,  and  Multiples 113 

XII.     Common  Fractions 119 

XIII.  Aliquot  Parts 158 

XIV.  Bills  and  Accounts 170 

DENOMINATE   NUMBERS 

XV.     Denominate  Quantities 191 

XVI.     Practical  Measurements 201 

PERCENTAGE   AND   ITS   APPLICATIONS 

XVIL     Percentage .231 

XVIII.     Commercial  Discounts 246 

XIX.     Gain  and  Loss 256 

XX.     Marking  Goods 264 

XXI.     Commission  and  Brokerage 270 

V 


vi  PEACTIOAL  BUSINESS  ARITHMETIC 

CHAPTER  PAGE 

XXIL     Property  Insurance 277 

XXIII.  State  and  Local  Taxes       .         .       •  .         .         .         .  286 

XXIV.  Customs  Duties 291 

INTEREST    AND   BANKING 

XXV.     Interest 300 

XXVI.     Bank  Discount       .         .         .         .         .         .         .         .326 

XXVII.     Partial  Payments 338 

XXVIII.     Bankers'  Daily  Balances 346 

XXIX.     Savings-bank  Accounts         .         .         .         .         .         .  349 

XXX.     Exchange 354 

EQUATIONS   AND    CASH   BALANCE 

XXXI.     Equation  of  Accounts 384 

XXXIL     Cash  Balance 393 

DIVIDENDS   AND   INVESTMENTS 

XXXIIL     Stocks  and  Bonds 396 

XXXIV.     Life  Insurance      •         . 420 

PARTITIVE    PROPORTION,   PARTNERSHIP,    AND   STORAGE 

XXXV.     Partitive  Proportion  and  Partnership  .         .         .  426 

XXXVL     Storage 443 

APPENDIX  A 

Adding  Machines     .........  449 

APPENDIX  B 

Tables  of  Measures  and  Business  Abbreviations  .         .  451 


INDEX 457 


PRACTICAL  BUSINESS  ARITHMETIC 


PRACTICAL  BUSINESS  ARITHMETIC 

FUNDAMENTAL   PROCESSES 


CHAPTER  I 

INTRODUCTION 

1.  The  student  who  is  prepared  to  study  business  arithmetic 
must  be  famihar  with  the  ordinary  symbols  used  in  the  state- 
ment or  the  sokition  of  problems;  he  must  have  the  ability  to 
read  and  to  write  numbers  with  facility;  he  must  know  the 
fundamentals,  and  he  must  be  able  to  perform  ordinary  opera- 
tions in  United  States  money,  and  in  both  common  and  decimal 
fractions. 

2.  In  this  course  in  business  arithmetic  one  learns  many 
simple  methods  for  handling  numbers  and  solving  problems, 
and  the  adaptation  of  arithmetic  to  important  business  operations ; 
he  also  acquires  skill,  rapidity,  and  accuracy,  and  he  learns  how 
to  prove  his  own  work,  thus  developing  self-reliance.  Because 
arithmetic  deals  with  the  problems  of  the  home  as  well  as  the 
business  office,  the  study  of  its  practical  and  everyday  features 
increases  one's  knowledge  of  the  usages,  the  phraseology,  and 
the  literature  of  business  and  commerce. 

3.  Much  attention  is  given,  in  the  text,  to  the  fundamental 
processes,  for  these  are  at  the  foundation  of  all  arithmetic.  One 
must  acquire  a  high  degree  of  accuracy  and  speed  in  the  hand- 
ling of  these  fundamentals  if  he  is  to  achieve  any  marked  degree 
of  success  in  his  subsequent  work. 

The  text  contains  an  unusual  amount  of  material  for  the  student's  work, 
and  portions  of  it  may  be  omitted,  at  the  discretion  of  the  instructor,  if  the 
advancement  of  the  class  warrants  it. 

1 


CHAPTER   II 

NOTATION  AND  NUMERATION 
ORAL  EXERCISE 

1.  How  many  different  figures  are  used  to  express  numbers  ? 

2.  What  is  the  meaning  of  the  syllable  teen  in  the  numbers 
from  13  to  19  inclusive  ? 

3.  What  is  the  meaning  of  the  syllable  ty  in  such  numbers 
as  20,  30,  40,  45,  75,  87,  96  ? 

4.  What  name  is  given  to  10  tens?  to  10  hundreds?  to  1000 
thousands?  to  1000  millions? 

5.  In  7,  70,  700,  7000,  and  70,000  how  does  the  7  change  in 
value  ?    In  7007  how  do  the  values  of  the  7's  compare? 

6.  What  is  the  value  of  the  cipher  in  any  number  ?  Why  is 
it  used  ?     Explain  the  use  of  the  ciphers  in  900,905. 

7.  Upon  what  two  things  does  the  value  of  a  figure  depend  ? 
Illustrate  your  answer,  using  the  number  121,000,121. 

8.  Mention  five  things  that  are  counted  in  thousands  ;  three 
things  that  are  counted  in  millions  ;  two  things  that  are  counted 
in  billions.      Can  you  think  of  any  use  for  trillions  ? 

9.  Read  aloud  the  following  : 

a.  During  a  smgle  year  the  coinage  department  of  the  United 
States  government  received  from  the  superintendent  1,193,100 
standard  ounces  of  gold  coin,  from  which  was  produced  standard 
ounces  of  coin  of  the  value  of  S6, 369, 090.  During  the  same 
period  the  coiner  also  received  9,189,533  standard  ounces  of 
silver  for  coinage. 

h.  In  the  United  States  Bureau  of  Engraving  and  Printing 
there  are  printed  yearly  about  70,000,000  sheets  of  United 
States  notes,  certificates  of  deposit,  bonds,  and  national  cur- 
rency to  the  amount  of  about  S500, 000,000.  In  addition  to 
this  there  are  printed  more  than  10,000,000,000  postage  stamps. 

2 


NOTATION   AND   NUMERATION 


THE  ARABIC   SYSTEM 

4.  This  is  the  common  system  of  notation.  It  is  generally 
called  the  Arabic  system  because  the  numerals  which  it  employs 
were  introduced  into  Europe  by  the  Arabs. 

The  Arabic  numerals  1,  2,  3,  and  so  on  to  9  originated  in  India  about  2000 
years  ago.  When  only  these  numerals  were  used,  the  system  proved  to  be  cum- 
bersome, and  all  mathematical  operations  involved  great  difficulty.  About 
1200  years  ago  the  cipher  0  was  added,  thus  making  a  system  sufficiently 
ample  and  simple  for  ordinary  purposes  of  analysis  and  investigation.  The 
Arabs  introduced  the  system  into  Europe  in  the  twelfth  century,  but  it  was 
not  until  about  300  years  later  that  it  displaced  the  clumsy  Roman  system. 

5.  The  distinctive  feature  of  the  Arabic  system  is  the 
place  value  of  the  numerals  employed.  The  value  of  an  Arabic 
numeral  depends  as  much  upon  its  place  in  the  number  as 
upon  its  simple  or  digit  value. 

Thus,  in  the  Roman  system,  VIl  =  5  +  1  +  1.  In  the  Arabic  system, 
511  =  5  hundreds  +  1  ^en  +  1.  5  has  not  only  the  unit  value  Jive,  but  also 
the  place  value  hundreds;  and  the  1  following  has  not  only  the  unit  value 
one,  but  also  the  place  value  ten, 

6.  The  successive  places  a  figure  may  occupy  in  a  number 
are  called  orders  of  units. 

7.  Orders  of  units  increase  from  right  to  left  and  decrease 
from  left  to  right  in  a  tenfold  ratio.     Therefore, 

8.  The  Arabic  system  of  notation  is  properly  called  a 
decimal  system,  from  the  Latin  decern,,  meaning  ten. 

9.  A  comma  (separatrix)  or  a  greater  space  than  that  between 
other  figures  may  be  used  to  separate  a  number  into  periods. 

Thus,  twenty-five  thousand  four  hundred  twenty-one  may  be  written 
25,421  or  25  421. 


ORAL  EXERCISE 

Read  aloud  the  following  numbers : 

1.  92,482.  3.  375,214.  5.  8  217  000  214. 

2.  77,009.  4.  278,900.  6.  7  000  421817. 


4  PEACTICAL  BUSINESS  ARITHMETIC 

10.  For  convenience  in  reading,  the  successive  orders  of  units 
are  divided  into  groups  of  three  figures  each,  called  periods. 
The  first  four  periods  are  shown  in  the  following  numeration 
table.  The  number  used  for  illustration  is  sixty-seven  billion, 
four  hundred  twenty-one  million,  five  thousand,  two  hundred 
sixteen,  and  seven  hundred  fifty-one  thousandths. 

Numeration  Table 

Periods  :  Billions        Millions      Tliousands        Units  Thousandths 


2       '  £  2  ** 

Orders:  ,«!»'^„,!»      '^r/>"»      -o^w       S 


rt 


a    -s 


^S=3         sja        3530        ssa        £ 
WHP       WHt:)       WHti       ffiHt:)       Q 

6   7,     42   1,     00   5,     216      .      751 

11.  In  reading  integers  do  not  use  the  word  and.  In  deci- 
mal fractions  and  has  an  office  to  perform,  but  if  it  is  used  in 
reading  integers,  misunderstandings  may  occur. 

Thus,  400.011  is  read  four  hundred  and  eleven  thousandths ;  but 
.411  is  read  four  hundred  eleven  thousandths ;  and 
411.        is  read  four  hundred  eleven. 

WRITTEN  EXERCISE 

Write  in  figures  the  followiyig : 

1.  Six  million,  six  thousand,  five. 

2.  Seven  hundred  fifty-three  billion. 

3.  Four  million,  one  hundred  twenty-five. 

4.  Three  hundred  twenty-one  million,  six. 

5.  Three  million  four  dollars  and  five  cents. 

6.  Ten  billion,  one  thousand,  one  hundred  three. 

7.  Twenty-seven  and  one  hundred  twenty-five  thousandths. 

8.  Sixty-two  thousand  and  four  hundred  twenty-five  thou- 
sandths. 

9.  Three  million  four  hundred  twenty  thousand  one  dollars 
and  fifteen  cents. 


NOTATION   AND   NUMERATION  5 

12.    Integers  should  be  read  in  the  shortest  way  possible. 

Thus,   1946  should  be  read  nineteen  hundred  forty-six,  not  one  thousand 
nine  hundred  forty-six.      The  space  for  writing  the  amount  on  a  check, 


tJ^irst  >^atLonal  Mank 

^ay  to  the  order  o/ O^  ^,    >^^^i^^^:-^^-:^^..^>/ /^^(^"^ 


T^^C^^^^^^yQv^Cd^t^^^^^^^ 


note,  or  other  business  paper  is  generally  limited  to  one  line,  and  it  is  im- 
portant that  the  amount  be  expressed  in  the  fewest  words  possible. 

ORAL   EXERCISE 

Head  aloud  the  following  : 

1.  Rhode  Island  has  an  area  of  1250  sq.  mi.,  and  contains 
800,000  A.;  Ohio  has  an  area  of  41,060  sq.  mi.,  and  contains 
26,278,400  A. ;  California  has  an  area  of  153,360  sq.  mi.,  and 
contains  101,350,400  A.;  Texas  has  an  area  of  265,780  sq.  mi., 
and  contains  170,099,200  A. 

2.  Lake  Itasca,  the  source  of  the  Mississippi  River,  is  situated 
approximately  3160  mi.  from  the  sea;  it  is  1575  ft.  above  sea 
level.  The  Mississippi  River  is  navigable  for  a  distance  of  about 
2200  mi. ;  the  area  drained  by  this  river  and  its  tributaries  is 
estimated  at  1,244,000  sq.  mi. 

3.  The  area  of  the  United  States  is  approximately  3,025,600 
sq.  mi. ;  of  Alaska,  570,000  sq.  mi. ;  of  Russia  in  Europe,  includ- 
ing Poland,  2,060,940  sq.  mi. ;  of  Switzerland,  15,792  sq.  mi.- 

4.  The  area  of  Africa  is  estimated  at  11,500,000  sq.  mi. ;  the 
coast  line  approximates  16,000  mi.  in  length ;  the  Sahara  Desert 
has  an  area  of  2,000,000  sq.  mi.  The  greatest  length  of  Asia  is 
about  7500  mi.,  and  its  greatest  breadth  Is  about  5160  mi. 


6  PEACTICAL   BUSINESS   ARITHMETIC 

THE   ROMAN   SYSTEM 

ORAL   EXERCISE 

1.  Make  a  list  of  the  Roman  numerals  used  in  the  headings 
marking  the  divisions  of  this  book,  and  read  the  list  so  prepared. 

2.  What  symbol  ordinarily  appears  on  a  watch  face  for  four? 

13.  This  system  of  writing  numbers  is  called  Roman  notation 
because  it  was  first  used  by  the  Romans.  It  is  now  rarely 
used  except  for  numbering  books  and  their  parts,  for  writing 
inscriptions  on  buildings,  and  for  marking  the  hours  on  the 
dials  of  clocks  and  watches.      It  employs  seven  capital  letters  : 

I  V  X  L  C  D  M 

1  5  10  50  100  500  1000 

14.  Other  numbers  are  expressed  by  a  combination  of  these 
letters  on  the  general  principle  that 

A  combination  of  letters  arranged  from  left  to  right  m  the  order 
of  value  is  equal  to  the  sum  of  the  constituent  letters. 

15.  But  the  use  of  the  same  letter  four  or  more  times  is 
avoided  by  employing  the  sub-principle-  that 

When  one  letter  precedes  another  of  greater  value  the  value  of 
the  two  is  that  of  their  difference. 

Thus,  II  =  2  ;  Vni  =  8  ;  and  CCC  =  300.  But  IV  or  IIH  =  4  ;  XL  = 
40;  XC  =90;  and  CD  =  400. 

ORAL  EXERCISE 

1.  Multiply  twenty -seven  by  itself  in  Roman  numerals. 

2.  Why  is  the  Arabic  system  better  than  the  Roman  system  ? 

3.  Read  the  following  inscription:  MDCCCXLVIII  — 
Charlestown  High  School —  MOM VI. 

Nineteen  hundred  was  formerly  written  MDCCCC,  but  it  is  now  often 
written  MCM. 

4.  Read  the  following  numbers  of  chapters  in  a  book  :  XXIX, 
XXXVIII,  LXIX,  LII,  LXVII,  LXXVI,  LXXIX,  CLIII. 

5.  Read  the  following  numbers  of  years  :  MDCCXCV, 
MCMVII,  MDCCLXXVI,  MCMIX,  MDCCCXCVIII. 


NOTATION    AND   NUMERATION  7 

WRITTEN  EXfeRCISE 

1.  Write  in  the  Roman  system :   19,  88,  99,  124,  1907,  1910. 

2.  Write  the  largest  possible  number  using  the  six  follow- 
ing numerals :  1,  0,  8,  0,  9,  5. 

3.  Write  in  Arabic  numerals  the  following  number :  five 
billion,  two  hundred  seventeen  million,  two  hundred  ten  thou- 
sand, and  fifteen  thousandths. 

4.  Write  in  the  Roman  system  the  following  historical  years  : 
the  discovery  of  America ;  the  landing  of  the  Pilgrim  Fathers 
at  Plymouth ;  the  declaration  of  independence. 

5.  Write  in  Arabic  numerals  the  number  in  problem  3 
increased  by  two  hundred  seventy-one  and  four  hundred  fifteen 
thousandths  ;  diminished  by  two  thousand,  four  hundred  sixty, 
and  eleven  thousandths. 

16.  A  unit  is  a  standard  quantity  by  which  other  quantities 
of  the  same  kind  are  measured. 

The  simplest  form  of  a  unit  is  a  single  entire  thing  by  which  other  simi- 
lar things  can  be  measured  by  integral  enumeration.  Thus,  the  unit  of  dis- 
tance is  an  inch;  a  group  of  12  in.  taken  in  succession  is  a  foot;  3  ft.  is  a 
yard  ;  and  so  on. 

17.  Numbers  that  have  units  of  the  same  kind  are  called 
like  numbers. 

Thus,  ^12  and  $15,  and  8  hr.  and   3  hr.,  are  like  numbers. 

ORAL  EXERCISE 

Name  the  unit  in  each  of  the  folloudng : 
1. '  A  barrel  of  sugar  sold  by  the  pound. 

2.  A  car  load  of  apples  bought  by  the  barrel. 

3.  A  car  load  of  lumber  sold  by  the  thousand  feet. 

4.  Sixty-four  thousand  bricks  sold  by  the  thousand. 

5.  Forty  and  one-half  yards  of  carpet  sold  by  the  yard. 

6.  Twenty-five  hundred   pounds   of   beef   bought   by   the 
hundredweight. 

7.  When  the  value  in  a  five-dollar  gold  piece' is  thought  of, 
what  is  the  unit  ? 


CHAPTER   III 

UNITED    STATES    MONEY 

ORAL  EXERCISE 

Read  the  following  expressions^  supplying  the  missing  word  o 
words : 

1.  The  denominations  of  United  States  money  used  in  busi 
ness  are  dollars, ,  and , 

2. mills  or cents  equal  one  dollar. 

3.  The is  not  a  coin,  but  it  is  sometimes  used  in  mat 

ing  calculations. 

4.  The  first  two  figures  at  the  right  of  dollars  denote 

and  the  third  figure  denotes . 

5.  The  two  figures  denoting  cents  express of  a  dollar 

the  figure  denoting  mills  expresses of  a  dollar. 

6.  One  thousandth  of  a  dollar  is mill ;  seven  mills  ar 

of  a  dollar. 

7.  Fifteen  hundredths  of  a  dollar  are ;   nine  tenth 

of  a  dollar  are  nine  — —  or cents. 

8.  $25  = ^;    3700^  =  1 ;    f  1T.85  = ^;   4925 

=  $ ;   179  = 1 

9.  State  a  short  method  of  reducing  dollars  to  cents ;  dol 
lars  and  cents  to  cents  ;  cents  to  dollars. 

18.  The  following  kinds  of  currency  are  in  daily  use  in  tb 
United  States  at  the  present  time  :  gold  coins ;  silver  dollars 
subsidiary  coins  (small  change) ;  gold  certificates ;  silver  cer 
tificates ;  United  States  notes ;  United  States  Federal  Reservi 
notes ;  National  Bank  notes. 

The  coins  now  issued  by  the  United  States  government  are  as  follows 

1.  The  gold  double  eagle,  eagle,  half  eagle,  and  quarter  eagle. 

2.  The  silver  half  dollar,  quarter  dollar,  and  dime. 

3.  The  nickel  five-cent  piece  and  the  bronze  one-cent  piece. 


UNITED   STATES   MONEY  9 

19.  Gold  or  silver  in  bars  or  ingots  is  called  bullion. 
The  paper  money  of  the  United  States  is  at  present  as  follows  : 

1.  Gold  certijicates,  issued  for  gold  deposited  in  the  U.  S.  Treasury. 

2.  Silver  certificates^  issued  for  silver  deposited  in  the  U.  S.  Treasury. 

3.  United  States  notes  {greenbacks),  promises  of  the  government  to  pay  to 
the  holder  on  demand  a  definite  number  of  gold  or  silver  dollars. 

4.  National  hank  notes,  issued  by  national  banks  under  the  supervision 
of  the  National  Government. 

5.  Treasury  notes,  which  were  issued  for  silver  bullion  deposited  in  the 
U.  S.  Treasury.     These  notes  are  not  now  issued. 

6.  United  States  Federal  Reserve  notes. 

ORAL  EXERCISE 

1.  What  is  meant  by  money ^  currency^  legal  tender? 

In  such  exercises  as  the  above  the  student  should  not  try  to  repeat  defini- 
tions, but  should  explain  the  terms  in  his  own  way. 

2.  Name  the  gold  coins  of  the  United  States;  the  silver 
coins ;  the  paper  money ;  give  the  value  of  each  of  the  gold  coins. 

3.  Read  in  three  ways :  $4.8665;  $25,871;  $178,475. 

4.  Name  the  largest  gold  and  silver  coins  that  will  exactly 
express  each  of  the  following  amounts  :  $27.90;  $28.20;  $75.80. 

20.  When  it  is  desirable  to  express  United  States  money  in 
written  words,  the  cents  should  be  written  in  fractional  form, 
as  in  the  following  note : 


$  /  ^J'rP  ^^^                     New  yovkf         (l^^^^j^^^/^^   1 9. 
x:^^^^^x^^g^.^^<.<:^^ after  date  ^>^ 


the  order  of '^~X/?^^^^t^i^^^^  ArSl^^^:^..^^,^^^  


at  ■^r^k^.^^^L^^^J^J-^?-^.^^^^':^^^ 


Value  received 


No.  ^^  Due^^^r.V,/^  -r^  /7^.  r^^^^^^^rCi^ 


CHAPTER   IV 

ADDITION 
ORAL  EXERCISE 

1.  Find  the  sum  of  1,  2,  3,  7,  5,  9,  4,  8,  and  6. 

2.  Read  each  of  the  numbers  m  problem  1  increased  by  2  ; 
by  5  ;  by  3;  by  7  ;  by  8 ;   by  9 ;  by  17;   by  23. 

3..  Find  the  sum  of  8,  7,  9,  5,  6,  11,  and  12. 

4.  Read  each  of  the  numbers  in  problem  3  increased  by  12; 
by  15  ;  by  18;  by  24;  by  42;  by  19;  by  16. 

5.  Illustrate  what  is  meant  by  like  numbers. 

21.  Only  like  numbers  can  he  added. 

22.  To  secure  speed  and  accuracy  in  addition  name  results 
only  and  express  these  in  the  fewest  words  possible. 

Thus,  in  adding  2,  4,  7,  8,  3,  2,  and  8  say  6,  13,  21,  4,  6,  34;   do  not  say 
2  and  4  are  6  and  7  are  13  and  8  are  21  and  3  are  24  and  2  are  26  and  8  are  34' 


ORAL 

EXERCISE 

Name  the 

sum 

in  ( 

jacA 

of  the  followiyig  problems : 

1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

9.      10.    11. 

12. 

13. 

14. 

15 

3 

2 

2 

8 

1 

5 

8 

1 

3      5      5 

1 

3 

4 

2 

2 

1 

4 

2 

3 

2 

2 

3 

3      14 

7 

2 

5 

7 

1 

6 

3 

1 

6 

1 

3 

6 

4      6      4 

2 

1 

2 

3 

2 

8 

2 

2 

4 

3 

7 

4 

2      2      3 

7 

5 

8 

5 

8 

4 

1 

3 

4 

4 

4 

9 

8      7      2 

3 

2 

6 

4 

4 

8 

4 

4 

3 

7 

7 

5 

3      3      1 

4 

8 

4 

2 

5 

6 

3 

5 

2 

2 

3 

8 

6      2      0 

5 

2 

5 

1 

6 

0 

6 

2 

3 

1 

4 

2 

2      5      7 

2 

6 

3 

4 

3 

8 

1 

7 

7 

6 

1 

1 

1      1      7 

7 

1 

2 

3 

3 

6 

2 

2 

4 

2 

2 

4 

3      4      2 

1 

1 

1 

2 

2 

2 

3 

5 

1 

8 

3 

2 

2      3      1 

3 

8 

6 

2 

4 

1 

5 

1 

2 

3 

2 

4 

12      4 

4 

9 

8 

7 

10 


ADDITION  11 

23.  Addition  is  the  basis  of  all  mathematical  processes.  It 
constitutes  a  large  part  of  all  the  computations  of  business 
life  and  concerns,  to  some  extent,  every  citizen  of  to-day. 
Ability  to  add  rapidly  and  accurately  is  therefore  a  valuable 
accomplishment. 

24.  Rapid  addition  depends  mainly  upon  the  ability  to  group ; 
that  is,  to  instantly  combine  two  or  more  figures  into  a  single 
number.  In  reading  it  is  never  necessary  to  stop  to  name  the 
individual  letters  in  the  Avords.  All  the  letters  of  a  word  are 
taken  in  at  a  glance  ;  hence  the  whole  word  is  known  at  sight. 
Words  are  then  grouped  in  rapid  succession  and  a  whole  line 
is  practically  read  at  a  glance.  This  is  just  the  principle  upon 
which  rapid  addition  depends.  PVom  two  to  four  figures 
should  be  read  at  sight  as  a  single  number,  and  the  group  so 
formed  should  be  rapidly  combined  with  other  groups  until  the 
result  of  any  given  column  is  determined.  This  can  be  done 
only  by  intelligent,  persistent  practice. 

25.  The  following  list  contains  all  possible  groups  of  two 
figures  each. 

ORAL  EXERCISE 

Pronounce  at  sight  the  sum  of  each  of  the  following  groups  : 
abcdefghijklmno 
1.    112241334      3      14247 


1 

3 

1 

2 

1 

5 

2 

3 

2 

6 

7 

3 

5 

6 

7 

2.    8 

9 

8 

5 

6 

4 

5 

5 

7 

1 

5 

6 

6 

8 

9 

9 

9 

8 

5* 

1 

4 

3 

4 

2 

8 

6 

6 

9 

6 

1 

3.     8 

7 

7 

4 

9 

7 

6 

7 

5 

3 

2 

4 

5 

7 

6 

2 

3 

5 

8 

3 

8 

7 

9 

9 

8 

9 

9 

8 

4 

2 

The  above  exercise  may  be  copied  on  the  board  and  each  student  in  turn 
required  to  name  the  results  from  left  to  right,  from  right  to  left,  from  top 
to  bottom,  and  from  bottom  to  top.  The  drill  should  be  continued  until 
the  sums  can  be  named  at  the  rate  of  150  per  minute.  This  is  the  first 
and  most  important  step  in  grouping. 


12 


PRACTICAL   BUSINESS   ARITHMETIC 


ORAL  EXERCISE 

Name  the  sum  in  each  of  the  following  problems  : 


1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

9. 

10. 

11. 

12. 

13. 

14. 

15 

6 

7 

3 

5 

6 

7 

9 

9 

9 

1 

2 

5 

8 

2 

8 

3 

1 

4 

2 

4 

7 

9 

8 

8 

4 

7 

2 

3 

7 

2 

8 

7 

7 

5 

8 

2 

5 

9 

4 

5 

8 

3 

5 

4 

1 

7 

9 

6 

9 

3 

9 

8 

4 

7 

1 

1 

7 

9 

5 

9 

3 

8 

5 

3 

8 

1 

6 

4 

9 

2 

6 

5 

7 

3 

4 

9 

4 

7 

7 

2 

9 

8 

5 

1 

3 

5 

7 

6 

5 

5 

5 

6 

6 

8 

2 

4 

4 

3 

6 

3 

6 

8 

7 

4 

6 

5 

6 

5 

5 

7 

5 

4 

2 

1 

3 

6 

4 

9 

4 

8 

2 

3 

2 

1 

1 

2 

3 

1 

1 

2 

5 

3 

8 

1 

9 

4 

3 

3 

1 

4 

2- 

1 

5 

6 

4 

5 

9 

7 

6 

6 

Name  tlie  results  only  and  make  groups  of  two  figures  each.  Thus,  in 
problem  1,  beginning  at  the  bottom  and  adding  up,  say  6,  16,  28,  43,  52. 

16-45.  Add  the  numbers  in  the  exercise  on  page  10  by 
groups  of  two  figures  each. 

26.  It  is  practically  as  easy  to  add  54  and  9,  59  and  6,  etc., 
as  it  is  4  and  9,  9  and  6,  etc.  4  and  9  are  always  equal  to  1 
ten  and  3  units, and  9  and  6  to  1  ten  and  5  units.  Hence  in 
adding  54  and  9  think  of  the  tens  as  increased  by  1,  call  the 
units  3,  and  the  result  is  63 ;  in  adding  59  and  6  think  of  the 
tens  as  6,  the  units  as  5,  and  the  result  as  QS, 

ORAL  EXERCISE 

Pronounce  at  sight  the  sum  of  each  of  the  following  groups : 
1.  27    48    59    77    58    52    59    75    95    84    39    59    84    76    91 


7 

8 

6 

8 

7 

8 

8 

6 

9 

7 

_6 

5 

9 

8   8 

2.  75 

59 

77 

88 

74 

23 

24 

44 

89 

78 

67 

37 

BQ 

58  68 

8 

9 

9 

5 

6 

8 

9 

9 

9 

9 

9 

7 

7 

4   5 

3.  37 

49 

38 

37 

45 

95 

98 

87 

54 

72 

63 

42 

73 

97  88 

5 

8 

7 

6 

9 

8 

7 

7 

9 

9 

8 

9 

8 

5  _9 

ADDITION  13 

27.  In  combining  numbers  between  10  and  20  think  of  them 
as  one  ten  and  a  certain  number  of  units  and  not  as  a  certain 
number  of  units  and  1  ten. 

Thus,  in  combining  17  and  18  think  of  28  and  7,  or  35;  in  combining  19 
and  15  think  of  29  and  5,  or  34 ;  and  so  on. 

ORAL  EXERCISE 

Pronounce  at  sight  the  sum  of  each  of  the  following  groups : 
abode        fghi        jklmno 
1.  12    17    12    16    11    12    18    16    17    11    19    13    18    12    17 

l^lll^l^lllll^l^l^  —  1^  —  3^5ti    — 

2.13  11  15  19  14  19  17  15  13  19  16  14  18  18  12 
l^lj6]^U151^1^1^ni^U14111519 

3.  11  17  12  17  15  15  12  18  16  14  19  14  19  17  11 

nui^i^ni5n]^]^i3i^i^i^iii5 

The  above  exercise  contains  all  combinations  possible  with  the  numbers 
from  11  to  19  inclusive.  Drill  on  the  exercise  should  be  continued  until  re- 
sults can  be  named  at  the  rate  of  120  per  minute. 

28.  Numbers  between  10  and  20  may  be  combined  with  num- 
bers above  20  in  practically  the  same  manner  as  in  §  27 

Thus,  in  adding  62  and  12  think  of  72  and  2,  or  74;  in  adding  79  and  17 
think  of  89  and  7,  or  96. 

ORAL  EXERCISE 

Pronounce  at  sight  the  sum  of  each  of  the  following  groups: 
1.  25    48    59    87    91    75    86    75    48    78    57    89    37    56    75 
17    17    16U1^1^1^1216131614171814 

2.29    47    83    92    36    54    59    78    67    92    77    86    53    78    85 
13    14    19    14    19    13    18    15    13    13    19    19    17    14    14 

3.  31    32    45    69    74    95    98    92    96    87    86    34    43    64    38 
19    17    19    15      8    18    14    19    15    17    19    18    18    19    17 


14  PRACTICAL   BUSINESS   ARITHMETIC 

ORAL  EXERCISE 

1.  Count  by  7's  from  1  to  85. 

Solution.     8,  15,  22,  9,  36,  43,  50,  7,  64,  71,  8,  85. 

Count  hy : 

2.  2's  from  39  to  55.  14.  8's  from  10  to  138. 

3.  5's  from  11  to  86.  15.  7's  from  19  to  152. 

4.  6's  from  15  to  63.  16.  6's  from  20  to  128. 

5.  5's  from  2  to  107.  17.  6's  from  15  to  111. 

6.  7's  from  11  to  60.  18.  9's  from  12  to  102. 

7.  8's  from  25  to  89.  19.  8's  from  17  to  113. 

8.  9's  from  31  to  112.  20.  7's  from  24  to  108. 

9.  8's  from  32  to  192.  21.  6's  from  27  to  117. 

10.  7's  from  18  to  102.  22.    4's  from  19  to  183. 

11.  6's  from  72  to  126.  23.    ll's  from  14  to  102. 

12.  9's  from  10  to  136.  24.    12's  from  17  to  161. 

13.  9's  from  17  to  152.  25.    13's  from  17  to  121. 
26.  Beginning  at  1  count  by  4's  to  17  ;  going  on  from  17 

count  by  7's  to  52  ;  from  52  count  by  9's  to  133  ;  from  133 
count  by  5's  to  158  ;  from  158  count  by  12's  to  206  ;  from 
206  count  by  13's  to  271. 

This  exercise  furnishes  one  of  the  best  possible  drills  in  addition,  and  it 
should  be  continued  until  the  successive  results  can  be  named  at  the  rate  of 
150  per  minute. 

29.  If  the  student  is  accurate  and  rapid  in  making  groups 
of  two  figures  each,  he  is  ready  for  practice  in  groups  of  three 
figures  each.  In  the  following  exercise  are  all  the  possible 
groups  of  three  figures  each. 

ORAL  EXERCISE 

Name  at  sight  the  sum  of  each  of  the  following  groups: 

4,  2,  and  3  should  be  thought  of  as  9  just  as  p-e-n  is  thought  of  as  pen. 

1.  419811318145178 
131223173314414 
332175   6   31941641 


ADDITION^ 

15 

2. 

1 

6 

1 

4 

1 

2 

1 

1 

1 

1 

7 

6 

9 

8 

1 

4 

1 

2 

1 

2 

2 

9 

1 

1 

6 

6 

6 

5 

5 

5 

9 

2 

5 

2 

3 

1 

1 

8 

7 

8 

1 

1 

1 

1 

7 

3. 

6 

5 

2 

5 

2 

3 

9 

2 

2 

2 

2 

6 

1 

1 

2 

1 

1 

3 

3 

3 

2 

2 

8 

7 

6 

5 

1 

1 

1 

2 

5 

5 

6 

2 

4 

3 

2 

2 

2 

2 

2 

1 

5 

4 

4 

4. 

3 

2 

1 

2 

2 

6 

2 

6 

5 

5 

7 

1 

1 

1 

1 

2 

2 

1 

7 

6 

8 

6 

2 

2 

2 

2 

1 

1 

6 

9 

2 

2 

3 

7 

9 

2 

7 

6 

9 

8 

5 

2 

1 

9 

9 

5. 

9 

8 

9 

8 

7 

3 

4 

5 

6 

6 

5 

4 

3 

3 

4 

1 

1 

1 

1 

1 

5 

8 

7 

7 

7 

5 

4 

4 

4 

4 

8 

8 

7 

7 

7 

5 

4 

0 

9 

8 

6 

7 

9 

8 

6 

6. 

5 

6 

6 

9 

5 

7 

3 

4 

9 

6 

6 

8 

3 

3 

3 

5 

7 

6 

4 

4 

3 

4 

4 

4 

8 

7 

4 

9 

4 

4 

5 

7 

9 

9 

4 

4 

6 

4 

8 

6 

6 

8 

9 

5 

4 

7. 

3 

4 

6 

9 

8 

5 

4 

3 

3 

2 

3 

3 

4 

5 

8 

8 

7 

6 

9 

9 

9 

7 

8 

3 

5 

3 

7 

7 

8 

8 

9 

9 

6 

9 

9 

9 

8 

8 

9 

6 

8 

9 

7 

9 

8 

8. 

8 

5 

4 

3 

3 

5 

2 

3 

3 

4 

5 

7 

7 

5 

4 

8 

8 

9 

8 

7 

2 

4 

3 

7 

6 

7 

9 

8 

7 

6 

9 

5 

6 

7 

3 

5 

9 

6 

7 

8 

9 

9 

9 

8 

7 

9. 

3 

3 

2 

2 

3 

3 

4 

5 

7 

9 

9 

9 

7 

3 

6 

6 

3 

4 

4 

3 

6 

6 

7 

8 

7 

6 

5 

6 

3 

4 

9 

5 

8 

7 

4 

8 

6 

7 

8 

7 

5 

4 

3 

3 

2 

10. 

2 

2 

3 

4 

5 

7 

2 

2 

3 

4 

5 

7 

9 

■6 

6 

4 

9 

6 

5 

6 

7 

4 

8 

5 

5 

6 

7 

9 

6 

5 

5 

9 

6 

8 

8 

8 

4 

9 

9 

7 

7 

7 

6 

5 

4 

11. 

8 

8 

9 

2 

2 

3 

4 

5 

6 

8 

8 

9 

6 

8 

7 

5 

8 

3 

3 

7 

5 

5 

5 

8 

8 

5 

4 

5 

7 

3 

3 

2 

2 

8 

9 

7 

5 

9 

9 

6 

5 

4 

3 

2 

2 

This  exercise  should  be  drilled  upon  until  the  sums  of  the  groups,  in  any 
order,  can  be  named  at  the  rate  of  120  per  minute. 


16  PRACTICAL   BUSINESS   ARITHMETIC 

ORAL  EXERCISE 

1-15.    Turn  to  the  exercise  on  page  10  and  find  the  sum  of 
the  numbers  given. 

Name  results  only,  and  make  groups  of  three  figures  each.     Thus,  in 
problem  1,  say  9,  23,  37,  43. 

Add  from  the  bottom  ujd  and  check  the  work  by  adding  from  the  top  down. 

Find  the  sum  in  each  of  the  following  problems : 

16.     17.     18.    19.    20.    21.    22.    23.     24.    25.    26.    27.     28.     29.     30. 

131422244   5   12954 
113331639574073 


1 

1 

4 

1 

5 

2 

2 

4 

5 

0 

2 

4 

1 

2 

1 

2 

1 

3 

1 

3 

1 

4 

1 

8 

8 

9 

2 

8 

0 

1 

2 

4 

1 

4 

6 

4 

5 

8 

3 

2 

0 

3 

0 

0 

6 

2 

2 

3 

8 

1 

1 

2 

1 

7 

1 

1 

5 

2 

5 

8 

2 

4 

2 

2 

2 

2 

2 

3 

8 

3 

5 

7 

2 

6 

1 

5 

2 

1 

4 

5 

3 

7 

6 

2 

7 

3 

7 

2 

6 

6 

1 

2 

9 

4 

3 

2 

3 

1 

8 

2 

2 

1 

6 

0 

7 

5 

1 

8 

3 

4 

2 

1 

2 

9 

9 

6 

7 

2 

3 

3 

3 

5 

2 

3 

3 

6 

9 

3 

3 

1 

2 

^  8 

2 

6 

3 

1 

3 

1 

3 

3 

1 

0 

5 

6 

3 

7 

0 

4 

1 

1 

3 

2 

7 

2 

4 

3 

0 

2 

8 

8 

4 

7 

2 

5 

9 

5 

4 

2 

5 

2 

4 

8 

5 

1 

2 

3 

3 

2 

3 

2 

2 

4 

1 

4 

4 

3 

2 

2 

0 

4 

3 

0 

5 

2 

1 

1 

2 

1 

2 

6 

6 

4 

4 

6 

6 

3 

6 

2 

5 

8 

8 

6 

2 

3 

3 

3 

5 

2 

4 

4 

3 

3 

2 

8 

2 

1 

2 

6 

5 

1 

1 

1 

3 

0 

5 

6 

1 

6 

2 

1 

4 

4 

1 

3 

7 

2 

9 

3 

7 

9 

1 

5 

7 

5 

7 

3 

5 

2 

2 

2 

6 

2 

2 

3 

1 

7 

3 

3 

7 

2 

4 

2 

5 

6 

1 

3 

1 

3 

0 

3 

2 

2 

1 

3 

1 

4 

2 

1 

2 

1 

2 

2 

7 

7 

7 

1 

1 

9 

2 

2 

9 

7 

2 

2 

3 

8 

3 

1 

2 

3 

9 

1 

2 

5 

2 

1 

3 

4 

4 

4 

1 

7 

7 

1 

0 

0 

8 

4 

8 

4 

2 

1 

3 

7 

3 

2 

5 

7 

6 

5 

5 

2 

4 

4 

3 

1 

6 

2 

1 

5 

5 

3 

2 

3 

2 

8 

1 

3 

6 

3 

2 

3 

1 

1 

2 

1 

1 

2 

1 

2 

1 

5 

7 

1 

1 

ADDITION 


17 


30.  It  is  always  an  advantage  to  find  groups  of  figures  aggre- 
gating 10  and  20  in  the  body  of  a  column. 

These  groups  should  be  added  immediately  to  the  sum  already  obtained 
by  simply  combining  the  tens  of  the  two  numbers.  It  is  not  a  good  plan, 
however,  to  take  the  digits  in  irregular  order  in  order  to  form  groups  of 
10  and  20. 

ORAL   EXERCISE 

Find  the  sum  in  each  of  the  following  problems^  taking  advan- 
tage of  groups  of  10  and  20  wherever  possible: 

5.   6.   7.   8.   9.  10.   11.  12.  13.  14.  15. 

525343   7   8  259 

554325   54  789 

56785   56  321 

79874   02  58   1 

24312369   7  525 


2. 


11  21  71  6 

9j  8j  3j  4 

71  41  51  1   8 

3J  6J  5j  9   2 


16.  17.  18.  19.  20.  21.  22.  23.  24.  25.  26.  27.  28.  29.  30. 


3J  8 


6   5 


31.  32.  33.  34.  35.  36.  37.  38.  39.  40.  41.  42.  43.  44.  45. 


6  6 

7  7 
7  8 
9  7 


2  7  6 

8  9  7 

9  9  4 
9  2  9 


46.  47.  48.  49.  50.   51.  52.  53.  54.  55.  56.  57.  58.  59.  60. 

38  42  25  35  46  14  21  12  18  29  57  17  13  14  15 


5  5  4 

7  6  8 

8  9  8 
4  5  5 


6  2  7 

6  7  2 

8  5  8 

2  3  6 


18  PRACTICAL   BUSINESS   ARITHMETIC 

31.  When  three  figures  are  in  consecutive  order  the  sum  may- 
be found  by  multiplying  the  middle  figure  by  3 ;  when  five 
figures  are  in  consecutive  order  the  sum  may  be  found  by  mul- 
tiplying the  middle  figure  by  5 ;  etc. ;  or  the  sum  of  any  num- 
ber of  consecutive  numbers  may  be  found  by  taking  one  half  the 
sum  of  the  first  and  last  numbers  and  multiplying  it  by  the 
number  of  terms. 

ORAL  EXERCISE 

By  inspection  find  the  sum  of: 
1.     2.       3.       4.       5.       6.       7.       8.       9.      10.     11.     12.     13.     14.     15. 

7  10    13    16    19    22    25    28    31    34     37     40     43     46     49 

8  11    14    17    20    23    26    29    32    35     38     41     44     47     50 
91215182124273033363942454851 

16.    17.    18.    19.    20.     21.    22.    23.    24.    25.     26.      27.     28.    29.     30. 

10  15  20  25  30  35  40  45  50  55  60  65     70  75  80 

11  16  21  26  31  36  41  46  51  56  61  66  71  76  81 

12  17  22  27  32  37  42  47  52  57  62  67  72  77  82 

13  18  23  28  33  38  43  48  53  58  63  68  73  78  83 
1419242934394449  54  59  64697479  84 

31.  32.  33.  34.  35.  36.  37.  38.  39.  40.  41.  42.  43.  44.  45. 

7  10  13  16  19  22  25  28  31  34  37  40  43  46  49 

8  11  14  17  20  23  26  29  32  35  38  41  44  47  50 

9  12  15  18  21  24  27  30  33  36  39  42  45  48  51 

10  13  16  19  22  25  28  31  34  37  40  43  46  49  52 

11  14  17  20  23  26  29  32  35  38  41  44  47  50  53 

12  15  18  21  24  27  30  33  36  39  42  45  48  51  54 

13  16  19  22  25  28  31  34  37  40  43  46  49  52  55 

14  17  20  23  26  29  32  35  38  41  44  47  50  53  56 

15  18  21  24  27  30  33  36  39  42  45  48  51  54  57 

16  19  22  25  28  31  34  37  40  43  46  49  52  55  58 

17  20  23  26  29  32  35  38  41  44  47  50  53  56  59 

32.  When  a  figure  is  repeated  several  times  the  sum  may  be 
found  by  multiplication. 


ADDITION 

19 

ORAL  EXERCISE 

By  inspection  find  the 

sum 

of: 

1. 

2 

3. 

4. 

5. 

6. 

7. 

8.       9. 

10. 

11. 

12. 

13. 

14. 

15. 

4 

3 

4 

5 

3 

7 

8 

8     15 

6 

7 

8 

15 

13 

9 

9 

7 

4 

5 

3 

7 

5 

7     15 

6 

8 

7 

14 

13 

8 

9 

8 

4 

5 

9 

7 

5 

9     15 

12 

7 

8 

15 

13 

8 

9 

8 

9 

5 

9 

8 

6 

9       8 

12 

7 

7 

14 

7 

9 

9 

8 

9 

9 

8 

8 

6 

9       8 

12 

7 

8 

15 

rr 

8 

16 

.   17. 

18. 

19. 

20. 

21. 

22. 

23.      24. 

25. 

26. 

27. 

28. 

29. 

30. 

3 

7 

4 

2 

7 

5 

12 

2       4 

6 

8 

9 

8 

5 

16 

3 

7 

4 

2 

7 

5 

5 

2       4 

6 

8 

9 

8 

5 

16 

3 

7 

4 

2 

4 

5 

5 

2       4 

6 

8 

9 

8 

5 

16 

2 

2 

7 

8 

4 

4 

5 

3       5 

4 

3 

5 

8 

5 

16 

2 

2 

7 

-8 

2 

4 

5 

3       5 

4 

3 

5 

8 

5 

20 

2 

2 

7 

8 

2 

4 

5 

3       5 

4 

3 

5 

9 

8 

1 

33.  In  all  written  work  make  plain,  legible  figures  of  a 
uniform  size,  write  them  equal  distances  from  each  other, 
and  be  sure  that  the  units  of  the  same  order  stand  in  the 
same    vertical  column. 

/     Z     ^     ^    cr     ^    y    ^    f    ^ 

34.  Many  of  the  errors  that  occur  in  business  are  in  simple 
addition.  Errors  in  addition  result  from  two  main  causes : 
irregularity  in  the  placing  of  figures ;   poor  figures. 

35.  In  business  it  is  important  that  figures  be  made  rapidly ; 
but  rapidity  should  never  be  secured  at  the  expense  of  legibility. 

WRITTEN  EXERCISE 


Co'py  and 

find  the 

sum  of: 

1. 

2. 

3. 

4. 

5. 

6. 

1745 

1842 

1249 

4271 

6229 

1481 

1862 

1695 

1810 

8614 

4813 

1862 

7529 

4716 

6241 

9217 

7142 

4129 

8721 

8412 

1728 

8214 

6212 

2412 

20 


PKACTICAL   BUSINESS   ARITHMETIC 


7. 

8. 

9. 

10. 

11. 

12. 

4216 

2110 

4142 

1061 

4113 

4112 

8912 

8420 

4347 

1875 

8217 

1012 

4729 

1641 

1012 

6214 

8614 

1862 

8624 

1722 

1816 

1931 

1692 

1721 

4829 

1837 

4112 

1648 

1591 

1692 

6212 

4216 

4210 

1721 

1686 

1486 

4110 

4117 

1618 

1728 

2172 

4112 

4210 

1832 

4060 

1421 

1754 

1010 

36.  The  simplest  way  to  check  addition  is  to  add  the  columns 
in  reverse  order.  If  the  results  obtained  by  both  processes 
agree,  the  work  may  be  assumed  to  be  correct. 

37.  In  adding  long  columns  of  figures  it  is  generally  advis- 
able to  record  the  entire  sum  of  each  column  separately  ;  then 
if  interruptions  occur,  it  will  not  be  necessary  to  re-add  any  por- 
tions already  completed.  After  the  total  of  each  column  has 
been  found  the  entire  total  may  be  determined  by  combining 
the  separate  totals  of  the  columns. 

38.  The  best  way  to  test  the  accuracy  of  columns  added  in  this 
manner  is  to  begin  at  the  left  and  repeat  the  addition  in  reverse 
order.  The  entire  total  of  each  column  should  again  be  written 
and  the  complete  total  of  the  problem  found  by  adding  the  sepa- 
rate totals  of  the  several  columns.  If  the  results  obtained  by 
the  two  processes  agree,  the  work  may  be  assumed  to  be  correct. 

39.  Example.  Find  the  sum  of  54,669,  15,218,  36,425, 
45,325,  and  68,619.     Check  the  result. 

Solution.  Beginning  at  the  bottom  of  the 
right-hand  column,  add  each  column  in  regu- 
lar order  and  write  the  entire  totals  as  shown 
in  (a).  Beginning  at  the  top  of  the  left- 
hand  column  again  add  each  column  and 
write  the  entire  totals  as  shown  ih  (6).  Next 
add  the  totals  obtained  by  the  first  and 
second  additions  and  compare  the  results. 
Since  the  total  shown  by  (a)  is  equal  to  the 
total  shown  by  (6),  the  result,  220,256,  is  assumed  to  be  correct 
addition  should  be  carefully  checked. 


(^) 

54669 

(«) 

19 

15218 

36 

28 

36425 

12 

21 

45325 

21 

12 

68619 

28 

36 

220256 

19 

220256 

220256 

med  to  be  correct.  All  work  in 

ADDITION  21 

WRITTEN  EXERCISE 

See  how  many  times  the  following  numbers  can  be  written  in 
one  minute.      Write  each  number  in  form  for  vertical  addition. 

1.  426579.  3.  i)7983.21.  5.  170812.34. 

2.  123987.  4.  $4080.91.  6.  ^^41182.50. 

Thus,  in  repeating  the  number  in  problem  1  write  it  as  follows ; 


^/  z   ^ 

^  7 

^ 

A^   Z     d 

^  7 

f 

A^  Z     ^ 

^  7 

^ 

^   Z      (^ 

S-  7 

f 

0^?^. 

Be  sure  that  the  spacing  between  the  lines  and  between  the  columns  is 
uniform.  Increase  the  speed  gradually  until  from  150  to  200  figures  can 
be  written  per  minute. 

40.  Skill  in  writing  figures  from  dictation  should  be  culti- 
vated. The  dictation  should  be  slow  at  first,  but  it  should  be 
gradually  increased  until  the  requisite  speed  is  acquired. 

41.  In  calling  off  numbers  to  another  great  care  should  be 
taken  in  order  that  no  errors  may  be  made.  In  reading 
United  States  money  the  word  dollars  should  be  called  with 
each  amount.  The  word  cents  may  be  omitted  in  all  cases 
except  where  there  are  no  dollars. 

Thus,  in  calling  $400.37  say /owr  hundred  dollars,  thirty-seven;  in  calling 
$25.11  say  ticentj/- five  dollars,  eleven;  in  calling  $1573.86  say  ffteen  hundred 
seventy-three  dollars,  eighty-six;  in  calling  $5.31  say  Jive  dollars,  thirty-one. 

WRITTEN  EXERCISE 

Write  from  dictation  and  find  the  sum  of: 

1.  $75.18, 1123.95,  $147.25,  $9.50,  $181.45,  $172.16,  $84.98, 
$314.95,  $49.10,  $69.90,  $312.60,  $415.90. 

2.  $3140.19,  $310.92,  $3164.96,  $3162.19,  $18.62,  $410.95, 
$690.18,  $10.75,  $3100.40,  $300.40,  $200.50,  $100.90,  $410.80, 
$100.85,  $310.60,  $80.90,  $399.80,  $412.60. 


22  PEACTICAL   BUSINESS   ARITHMETIC 

WRITTEN   EXERCISE 

Co'py^  find  the  sum.,  and  check  : 

1.  2.  3. 

.^/  C^Z^  C^.Z/     "^i^  Z^Zf^jTA^.^  Z    !^Z  /^/  6  Z  /.^// 

/J^jrCyr.^^  /  ZJ-  f  ^/  ^.^^  /  2  (^  Z/  V/.Cy 

3yf^Z(if./y  Z/  y  ^Z^J.^z^  Z/3  /A^yZ.c^3 

^yZ/z3^.z3  f  / 3  / ^z  C.6?^  /^(^ z  /  ^/.izy 

A^z/  z  1^  /  z.^j-  / zj-y z/  z.^^  fC^ry  (^r.^3 

/  ZA^f  Z  /  Z.^4^     /  3  Z  /  C^Z./  y     /  Z^Zz^y  z.A^Z 

y  zrzf /^A^.y  (>  Z/ z^ /  C> z  /.^^  yr^r63r.^r 
z/yyz/6.^zz  3  /^/  z^f.cp  ^  z/A^/Z(iz.^f 
li  yZ3  zz  ^y/zr  Z  /  /  zzZc^  /.^r  ry  i^yr^Zyi^  / 
Zzz^  r<^  zy./  ^  3  /  y^Zj-y.(^y  /  z  C  Zz/yy/^ 
Z_y^^£j^A^_Z_£^^Jy.^^  3^y_^Z^rAf_^ 


4.  5  6. 

// z  Cy  z^.^ajt  ^/  zy^z^z^.A^j^  ^/ Zs- /  ^ z^/.^^zz 

¥3y.zC  y^^/  Zcpzzy.yz  yz/z^<^.^A^ 

Z Z.y /  / Z  /^  c^j-^^.^z  zz/  /  z^ ^z.J"^ 

/.  ^f  Z/CzZ/zZ'.yy  /J-cz^(p^^.yr 

(^/Zy  ^ r^.A^z  /C/^y.fz  / y  C y z/ ^.3zz 

j~jZ/Cz/,yJ-  7Z/A^6.J~A^  ZzyZc^  /  ZC^ /^.ZS 

y/z.yr  /  z.ys-  /  zyf'C3.C^ 

yz./zz  /z^.fZ  V  zi^A^fz 

j~6y.rC  z/A^C'^/  yj'/Z(^yz.(zy 

y/.A^ii  3zCzzs:y/  / Cf  x/  ^ z.^^zz 

yzCy.zzz  zzrzi^^.^/  /yz/.yc? 

Cyzzz.y^  3(Z6^/.yf  ^/ li.ys 

/Zyyr.^y  y^.cz<i  (^yz/.y^ 

/zzz.C(p  /.yz  /zz.yj' 

^____________^^^^^£^       A^/Z^.yr.  zzzi>/.yy^ 


ADDITION  23 

7.  8.  9. 

f  /^JTJ  C.A^/  f  Z  (^  f^.yJ'  Z^/  1^  Z  /  A^.Zf 

(^r/Z.O(P  3  ^y  ry.^^  /  z  (^./  A^Z  /^.4^/ 

Z3  zy  /  ^./  r  /  (i  y  Zf.y^  /  c?  /  f  ^  zy.6^ 

yrz.y^r  /  r  y  xy.y^  yf/tsj.A^^ 

/zj-Cr.3^  3  yA^z  ^  /.A^z  yz//C^y^ 

zz  yyv^zyr  /  cp z  (^A^dP  ^.^y  J  r y  y ^^j ti 

z  (^ o^A<y^  ^ z/  A^j~y.yz  /y^/yz.A^^ 

zz  ^ ^y /.3y  y^z^ ^ y.^r  y/^^yjr.j-^ 

f'j  ^ z.^^  (,y z^ /  i^.Z^  /Z^/Z.A^c> 

A^Z  (^  tJ  ^.y^  J~Z./  z  cp y.cTA^  li  z/ /  zys 

rzy(:^A^-jj~  J  y  zy  z.zo  /  C  /  Cy  /  z.^z 

3d-y^rz.zo  y  z  ^  A^^.c? o  y^/iT.ys 

yyCo.^c?  yZA^J~.6f  /  (^  Z  /  y.y^ 

r  (^J~2  /.A^^  J  ^  cp  A^y.pzd  /  A^  /  yj-Z  /.Ca^ 

yj'^j  y  ^.^^  (^  y  z^/  /  <^.j-z  /  /  z  /  z/^  oyJ' 

/  (p /  (^ r.Z3.z^  y z / z  ^37/ /  6y(ry<^.cz 

^ z  y A^^./ z-  ^z/^7^.^/  y Zzz / 3 r.y^" 

A^r3/^.y^  yz/: /  <i  zy.  ^3  /  z  i^ A^z/.zii 

yzy  rj-y.^^  C Z  /  Z^i^.yj-  Z^/ y  ZZ/.C^z 

ZC  Z^rzyz/  Cy/zr.io  CyZ/^yJ' 

/  Z  <^  /  Z  y.A^jT  /  o  /  z  o  /  (i.3'y  z  /  /  /  (Z yA^.z^/ 

y  /^  f^j'Z./ y  y  y  z  ^  /  y.zy  y y  y  yj/:^,(Z>y 

/j/y/z./r  /  Z./  Z^  ZX  c^  yZ/Z(^y3 

Z3~ /  y Z  C.r(^  /  (p  /  A^ZyX3r  z^/ 3  zy./z/ 

^/^3~3z.zzj-  zz^/^^y.^A^  y3'yyr3.yC 

zZi^/A^.yz  Cyjyr.y^  /C/zC.A^y 

z/ ^  z  zr^z.zo  y  (p  /  Z^.yz  y  z  / Z.a^S 

yy^^z.^/z  (^y3~A^.r'y  zyyzCy./f 

6  r  o3~z.^^  /  z  C  y  ^  zC.j~A^  /  f'y  z^zy.ycp 

/zC/ZJ~.Cs  3z/C/A^.yc>  <^yZA^(iy<r 

3  y^r^.^^  /  6  Z3  C y.y q^  z^z /  z  C.ZSy 


24  PRACTICAL   BUSINESS   AEITHMETIC 

42.  Some  accountants  practice  adding  two  columns  at  once 
when  the  columns  are  short.  The  method  generally  employed 
is  similar  to  the  method  explained  for  combining  groups  in 
regular  addition. 

43.  Example.    Find  the  sum  of  83,  72,  89.  ^_ 

83 

Solution.    Beginning  at  the  bottom  and  adding  up,  think  of  89  and  rrn 

72  as  159  and  2,  or  161  ;  of  161  and  83  as  241  and  3,  or  244. 

In  adding  name  results  only.     Thus  say  159,  161,  ^41,  244. 


89 
244 


ORAL  EXERCISE 

By  inspection  give  the  sum  of  each  of  the  following  groups : 
1.       2.       3.        4.       5.       6.       7.       8.       9.     10.    11.    12.     13.    14.    15. 

43  64  52  37  65  38  52  85  93  68  58  76  83  57  62 
2518     295627     43673472754639472539 

16.     17.     18.      19.     20.     21.     22.    23.    24.    25.    26.    27.    28.    29.    30. 

53  52  61  34  91  68  48  24  78  54  94  57  92  76  43 
46433776134769    96'76353644373156 

31.     32.    33.    34.    35.     36.    37.    38.    39.     40.     41.     42.     43.     44.     45. 

65  44  46  48  67  44  53  25  54  46  33  16  67  83  88 
86  57  65  25  48  57  45  31  65  39  64  34  43  82  25 
7^21M3139216769878777254198  31 

horizo:n^tal  addition 

44.  In  some  kinds  of  invoicing  and  in  short-extending  the 
items  of  an  account  numbers  to  be  added  are  written  in  horizon- 
tal lines.  Much  time  may  be  saved  by  adding  these  numbers 
as  they  stand.  After  careful  practice  it  will  be  found  possible 
to  add  numbers  written  in  horizontal  lines  with  as  much 
facility  as  numbers  written  in  vertical  columns. 

45.  In  adding  numbers  written  horizontally  care  should  be 
exercised  to  combine  only  units  of  the  same  order.  It  is  gener- 
ally best  to  add  from  left  to  right  and  to  verify  the  work  from 
right  to  left.  Grouping  may  be  employed  to  advantage  in 
horizontal  addition. 


ADDITION  25 

WRITTEN  EXERCISE 

Copy  and  add  the  following  7iumhers  Iwrizontally.  Verify  the 
work. 

Thus,  in  problem  1,  beginning  at  the  left,  say  10,  20,  32,  52.  In  verifying 
the  work  from  the  right  say  20,  32,  42,  52. 

1.  8,  2,  1,  1,  7,  1,  4,  6,  2,  3,  8,  9. 

2.  7,  9,  6,  5,  4,  8,  7,  4,  3,  7,  3,  1,  3. 

3.  6,  2,  4,  8,  3,  1,  7,  6,  4,  2,  8,  9,  4,  2. 

4.  15,  23,  46,  83,  29,  35,  42,  15,  21,  26. 

5.  64,  48,  dG,  35,  47,  87,  32,  45,  67,  91. 

6.  52,  64,  86,  28,  .76,  41,  15,  32,  12,  87. 

7.  32,  48,  24,  62,  85, 14,  63,  54,  78,  94,  23,  45. 

8.  42,  76,  49,  81,  17,  42,  17,  19,  21,  43,  64, 17. 

9.  45,  48,  34,  46,  48,  53,  25,  42,  35,  56,  70,  10. 

10.  291,  196,  855,  578,  210,  354,  102,  232,  241,  162. 

11.  469,  388,  962,  764,  351,  899,  111,  232,  190,  175. 

12.  1525,  5025,  1(384^  3142^  gg^s,  1910,  23^2,  1013,  648^,  4010. 

It  is  frequently  desirable  to  express  dollars  and  cents  without  the  dollar 
sign  and  the  decimal  point.  This  may  be  done  by  slightly  raising  the  cents 
of  the  amount.     Thus,  $  17.17  may  be  written  IT^'^ ;  ^  2.08  may  be  written  2^^ 

13.  1525,  893,  488,  2184,   IQS5^  1846,  291*,  4460,  (3290,  846O,  4050. 

14.  76'5,  8497,  6705,  95'4,  68^3,  522i,  1325,  4218,  60^5,  80i3,  9062. 

46.  It  is  important  that  the  student  acquire  the  ability  to 
carry  a  series  of  numbers  in  mind.  The  following  exercises 
are  suggestive  of  what  may  be  done  to  cultivate  ability  in  this 
direction. 

The  dictation  suggested  should  not  be  slower  than  at  the  rate  of  one 
hundred  twenty  words  per  minute.  Nothing  should  be  written  by  the 
students  until  all  of  the  numbers  of  a  problem  have  been  called  by  the 
instructor ;  then  one  student  may  be  sent  to  the  blackboard  and  required 
to  write  the  numbers  from  memory.  If  the  numbers  are  correctly  written, 
the  instructor  may  require  another  student  to  give  the  sum  of  them  with- 
out using  pen  or  pencil.  The  numbers  may  be  written  on  the  board  in 
either  vertical  or  horizontal  order,  as  the  instructor  may  direct. 


26 


PRACTICAL   BUSINESS   ARITHMETIC 


ORAL  EXERCISE 

From  the  instructor's  dictation  find  mentally  the  sum  of  each  of 
the  following  problems  : 

147,  253,  179,  121. 
423,  517,  81,  49. 
255,  45,  89,  121. 
25,  65,  27,  133. 
S48,  $32,  S138. 
$135,  $275,  $418. 
$23,  $67,  $281. 
$284,  $36,  $245. 
133,  167,  29,  61. 
2319,  1681,  2335. 
3310,  2790,  1565. 
2740,  1365,  2135. 
2273,  1237,  1145. 
1432,  1058,  1210. 

WRITTEN  REVIEW  EXERCISE 


1. 

6,  9,  8,  4,  8,  6. 

15 

2. 

14,  17,  20,  5,  9. 

16 

3. 

24,  17,  16,  9,  5. 

17 

4. 

5,  6,  7,  1,  3,  8. 

18 

5. 

6,  2,  8,  1,  7,  4. 

19. 

6. 

364,  436,  657,  25. 

20. 

7. 

438,  212,  750,  64. 

21. 

8. 

859,  441,  769,  71. 

22. 

9. 

2140,  3160,  4000. 

23. 

10. 

200,  415,  600,  95. 

24. 

11. 

857,  643,  237,  500. 

25. 

12. 

$4150,  $4050,  $850. 

26. 

13. 

$5.15,  $2.15,  $6.70. 

27. 

14. 

$167.14,  $232.86,  $9. 

28. 

1.   Find  the  sum  of  all  the  integers  from  2165  to  2260  inclu- 


sive. 


2.    Find  the  sum  of  all  the  integers  from  1137  to  1200  inclu- 


sive. 


3.  Complete  the  following  sales  sheet.  Add  by  columns 
and  by  lines  and  check  the  work  by  adding  the  vertical  and 
horizontal  totals. 


Summary  of   Sales   for   Week   Ending    Aug. 

25 

Pine 

Oak 

Maple 

Spruce 

Walnut 

Cherry 

Total 

Monday 

1216 

18 

16161 

47 

649 

58 

860 

40 

315 

64 

186 

50 

Tuesday 

5160 

40 

3214 

90 

316 

40 

160 

50 

513 

80 

216 

54 

Wednesday 

6152 

18 

2150 

18 

163 

59 

430 

17 

968 

52 

756 

14 

Thursday 

1216 

18 

2160 

50 

130 

98 

115 

67 

413 

60 

314 

75 

Friday 

4160 

80 

1215 

40 

315 

16 

218 

90 

411 

60 

132 

75 

Saturday 

3165 

80 

2115 

72 

218 

50 

165 

37 

118 

50 

17 

05 

Total 

'  -a: 

/  ' 

ADDITION 


27 


4.    Add   the  following  by  columns  and  by  lines,  and  check 
tlie  work  by  adding  the  vertical  and  horizontal  totals  : 


21162 

49 

96218 

1245 

76 

54168 

97 

52 

19 

17(') 

19 

1278195 

52698 

13 

7529 

87 

95162 

87 

2104 

89 

7524 

16 

47612 

87 

6842 

23 

5948 

23 

76 

95 

87 

14 

2150 

49 

172  93 

1745 

86 

51276 

92 

18187 

95 

75 

19 

162 

14 

6290 

18 

9834 

18 

92923 

15 

25 

91 

162 

18 

14 

95 

754 

95 

2167 

92 

2584 

16 

9176 

92 

3164 

82 

1356 

05 

1314 

93 

7125 

95 

2167 

18 

2645 

97 

756 

92 

142 

18 

167 

42 

926 

44 

3167 

18 

75162 

19 

82195 

78 

72162 

18 

9165 

97 

168 

44 

7162 

95 

4167 

18 

7156 

95 

172 

18 

1 

56 

2 

15 

6843 

82 

3954 

05 

60 

65 

9 

18 

8 

85 

9162 

19 

5144 

65 

8162 

18 

91684 

57 

2416 

45 

1829 

32 

4217 

64 

1492 

95 

8647 

64 

168 

94 

257 

16 

417 

86 

952 

17 

347 

18 

5.  Complete  the  following  sales  sheet.  Add  by  columns 
and  by  lines  and  then  check  the  work  by  adding  the  vertical 
and  horizontal  totals. 


Summary   of   Clerks'    Daily   Sales 


Names  of  Clerks 

Monday 

Tuesday 

Wednesday 

Thursday 

Friday 

Saturday 

Total 
FOR  Week 

J.  E.  Snow 

167 

18 

194 

67 

98 

46 

241 

80 

175160 

314 

90 

W.  B.  Moore 

78 

20 

65 

14 

50 

42 

60 

93 

51 

19 

64 

86 

T.  B.  Welch 

112 

40 

118 

64 

192 

40 

146 

18 

110 

50 

140 

12 

E.  H.  Ross 

164 

90 

143 

18 

192 

64 

214 

10 

110 

60 

190 

18 

Minnie  Davis 

165 

19 

214 

78 

120 

42 

167 

18 

164 

27 

140 

51 

Ada  Benton. 

68 

49 

90 

81 

64 

75 

120 

14 

142 

16 

60 

90 

Elmer  S.  Frey 

240 

18 

920 

41 

718 

52 

167 

59 

840 

72 

143 

86 

Joseph  White 

22 

49 

72 

86 

51 

47 

62 

14 

91 

26 

72 

15 

Margaret  Dix 

47 

26 

91 

18 

21 

64 

18 

42 

61 

19 

64 

86 

F.  0.  Beck 

127 

16 

95 

27 

114 

82 

162 

15 

102 

15 

112 

61 

L.  0.  Avery 

214 

91 

218 

46 

920 

41 

172 

14 

152 

86 

142 

71 

B. W.  Snyder 

162 

14 

153 

46 

118 

64 

162 

14 

182 

15 

69 

58 

Ella  Harding 

21 

27 

18 

92 

17 

65 

28 

64 

59 

18 

72 

41 

Carrie  Simpson 

21 

18 

45 

30 

10 

98 

42 

41 

20 

68 

75 

98 

W.  F.  Baldwin 

162 

10 

114 

80 

115 

90 

116 

84 

117 

41 

200 

60 

E.  0.  Burrill 

84 

90 

90 

10 

116 

80 

114 

30 

65 

20 

300 

75 

Total 

6.    On  the  page  following  are  a  number  of  inventory  exten- 
sions ;  find  the  footing  of  each. 


28  PRACTICAL   BUSINESS   ARITHMETIC 

Each  column  should  be  added  in  approximately  three  minutes. 


a. 

h. 

c. 

$1628.45 

S1743.19 

$2065.32 

176.22 

78.91 

145.55 

453.26 

1011.45 

28.49 

1102.65 

125.60 

.      217.86 

45.22 

101.25 

207.41 

143.51 

74.24 

1078.44 

55.68 

212.35 

45.60 

425.70 

338.90 

256.85 

119.45 

227.83 

194.61 

7.15 

46.21 

112.45 

89.52 

117.25 

34.65 

48.75 

57.81 

133.27 

170.25 

9.11 

24.13 

613.81 

764.35 

495.34 

1203.05 

88.75 

6.17 

327.16 

401.19 

98.75 

654.32 

1145.22 

856.21 

108.17 

366.18 

1408.95 

75.45 

201.13 

376.23 

9.58 

64.33 

112.50 

142.53 

8.78 

56.40 

189.70 

89.56 

76.50 

20.65 

192.35 

244.56 

673.13 

98.75 

^339.54 

120.06 

320.16 

87.40 

65.34 

135.20 

467.80 

753.25 

846.18 

515.05 

371.10 

1904.76 

287.01 

69.16 

128.44 

301.04 

231.06 

473.08 

1654.23 

503.44 

95.16 

270.15 

78.42 

143.65 

69.40 

250.21 

54.30 

355.11 

2859.89 

1756.84 

742.13 

ADDITION  29 


WRITTEN   EXERCISE 


Each  of  these  groups  should  be  added  in  approximately  one  minute. 

1.  2.                                                   3. 

6,354,276,742  6,917,408,583  8,632,714,509 

5,116,433,854  5,880,734,112  6,875,352,272 

8,446,750,284  6,538,922,553  8,539,168,753 

2,141,991,648  7,543,276,445  8,335,674,912 

4.653.752.816  6,441,819,263  5,321,841,174 

3.256.851.539  2,574,438,911  2,435,627,819 

5.462.175.255  4,156,717,549  1,546,721,973 
6,435,621,953  1,817,908,667  5,167,534,217 
4,717,880,945  6,745,243,517  4,576,819,054 
5,601,523,764  3,546,798,212  4,151,762,492 

4.  5.                                                    6. 

2,334,515,637  5,432,317,892  6,453,615,809 

5.734.516.772  6,534,31 7,865  4,576,879,253 

7.354.618.227  4,531,841,962  2,432,653,274 
3,542,618,906  3,132,341,264  7,819,457,836 
5,115,616,874  4,651,272,335  1,918,776,425 

7.175.437.256  3,256,728,143  5,327,731,224 

1.735.273.540  1,830,925,165  4,532,551,243 

8.134.556.773  2,543,175,213  5,231,605,228 
3,115,617,221  3,413,214,605  7,615,257,818 
3,255,617,711  5,443,216,448  5,663,338,119 

7.  8.                                                    9. 

4.334.561.228  3,653,212,716  4,176,234,562 
1,765,371,442  7,661,823,394  5,934,736,548 
9,717,632,461  5,749,287,716  6,254,817,259 
5,616,727,640  3,264,723,445  1,218,735,143 

2.615.431.817  2,845,367,621  7,342,235,907 
4,256,713,332  4,256,443,486  6,543,217,194 
3,078,395,668  7,254,563,823  2,546,718,911 
7,845,446,772  9,117,224,383  3,664,293,189 
8,250,114,337  1,493,786,332  9,226,847,821 


30  PEACTICAL  BUSINESS  ARITHMETIC 

A  WRITTEN  REVIEW  TEST 

Write  the  following  problems  from  dictation,  and  then  complete 
the  work.  Time,  approximately,  thirty  minutes,  including  the  dicta- 
tion.   Add  the  following : 

1.  2. 


23,418 

17,546 

28,356 

43,572 

43,621 

23,811 

32,718 

21,471 

71,892 

32,264 

10,918 

37,509 

22,457 

31,542 

27,354 

42,311 

34,256 

45,623 

45,612 

20,175 

41,243 

54,819 

33,452 

75,604 

44,172 

22,716 

31,174 

70,219 

34,523 

45,613 

44,530 

28,332 

31,113 

41,414 

45,517 

37,743 

20,125 

13,064 

50,197 

22,508 

62,157 

93,845 

29,875 

45,612 

In  problems  3  and  4  add  by  columns  and  then  by  lines,  and  check 
the  work  by  adding  the  vertical  and  horizontal  totals. 


3. 


542 

236 

? 

.  123 

235 

? 

437 

653 

? 

947 

834 

? 

572 

246 

? 

174 

215 

9 

445 

354 

? 

313 

208 

? 

236 

716 

? 

364 

312 

? 

423 

394 

? 

252 

733 

? 

347 

616 

? 

243 

317 

? 

455 

494 

? 

203 

406 

? 

337 

651 

? 

543 

392 

? 

453 

283 

? 

527 

618 

? 

624 

912 

? 

624 

483 

? 

538 

496 

? 

713 

626 

? 

712 

324 

? 

235 

439 

? 

? 

? 

? 

? 

? 

? 

CHAPTER   V 

SUBTRACTION 
ORAL  EXERCISE 

State  the  number  that^  added  to  the  smaller  yiumher^  makes  the 
larger  one  in  each  of  the  following : 

1.   344567889, 9   99887 
12   13   23   3   23164412 


2. 

12 

11 

12 

11 

12 

11 

12 

11 

10 

11 

10 

11 

10 

12 

10 

9 

2 

3 

9 

8 

3 

4 

8 

4 

7 

6 

4 

7 

5 

3 

3. 

18 

17 

16 

17 

16 

15 

14 

15 

14 

13 

13 

16 

15 

14 

13 

9 

8 

7 

9 

8 

6 

9 

7 

.  8 

4 

7 

9 

8 

5 

_9 

4. 

13 

14 

14 

15 

16 

17 

18 

18 

19 

19 

19 

19 

18 

18 

17 

11 

12 

11 

13 

12 

13 

13 

12 

13 

11 

16 

14 

14 

11 

12 

5. 

22 

21 

22 

21 

22 

21 

22 

21 

20 

21 

20 

21 

20 

22 

20 

19 

12 

13 

19 

18 

13 

14 

18 

14 

17 

16 

14 

17 

15 

13 

6. 

38 

27 

26 

37 

26 

35 

44 

25 

34 

53 

43 

36 

45 

54 

73 

29 

18 

17 

29 

18 

26 

39 

17 

28 

44 

37 

29 

38 

45 

69 

7. 

42 

51 

72 

81 

92 

71 

32 

41 

70 

61 

90 

81 

30 

62 

50 

39 

42 

63 

79 

88 

63 

24 

38 

64 

57 

86 

74 

27 

bb 

47 

47.    A  parenthesis  (  )  signifies  that  the  numbers  included 
within  it  are  to  be  considered  together.     A  vinculum  has 

the  same  signification  as  a  parenthesis. 

Thus,  15  -  (4  +  2),  or  15  -4  +  2  signifies  that  the  sum  of  4  and  2  is  to 
be  subtracted  from  15. 

31 


32 


PRACTICAL   BUSINESS   ARITHMETIC 


48.    Examples,    i.    Find  the  difference  between  849  and  162. 

Solution.  2  from  9  leaves  7.  6  cannot  be  subtracted  from  4,  but  6  q^q 
from  14  leaves  8.  Since  1  of  the  8  hundreds  has  been  taken,  there  are  but  -«  ^^ 
7  hundreds  remaining.     1  from  7  leaves  6.  "^ 

Check.     687  +  162  =  849.  687 

The  above  is  a  common  method  of  subtraction.  For  practical  computation, 
however,  the  "making  change"  method  is  best.  It  is  easily  understood  and 
is  much  more  rapid  when  once  learned.  The  "making  change"  method  is 
illustrated  in  the  following  example  and  solution. 

2.    Find  the  difference  between  7246  and  4824. 

Solution.     Think    "4  +  2  =6,"  and  write   2;    "2  +  2  =  4,"  and        7246 

write  2  ;  "  8  +  4  =  12,"  and  write  4  ;  "  1  and  4  +  2  =  7,"  and  write  2.      4824 

Check.    2422  +  4824  =  7246.  "2422 


ORAL  EXERCISE 


1.  16+ 23  +  ?  =  54? 

2.  27  + 14  +  ?  =  72,? 

3.  17 +  36  +  ?  =62? 

4.  19 +  17 +  12  +  ?  =57? 

5.  25 +  14 +  11+?  =  75? 

6.  18 +  17 +  16  +  ?  =  70? 


7.  16  +  18  +  16  =  25  +  ? 

8.  72  +  17  +  11  =  37  +  ? 

9.  14  +  18  +  38  =  42  +  ? 

10.  12 +  16 +  12 +  14+?  =  75? 

11.  16 +  15 +  19 +  15+?  =  93? 

12.  18 +  17 +  15 +  29+?  =  98? 


WRITTEN  EXERCISE 

1.    Without  copying   the    individual  problems,  find  quickly 
the  sum  of  the  twenty  differences  in  the  following: 


12140.50 
714.23 

85500.89 
2799.14 

$9275.17 
842.99 

17514.85 
721.92 


14157.50 
1236.80 

11624.14 

957.80 

-12446.80 
1321.44 

17291.80 
1642.95 


$5000.24 
249.17 

11985.72 
645.92 

$3169.14 

874.36 

11756.92 
921.74 


$9000.72 
1246.18 

$1379.54 
923.18 

$3156.19 
1400.72 

$8721.13 
2049.79 


$3145.62 
2000.79 

$1742.18 
842.16 

$4756.83 
2738.44 

$1872.14 
742.12 


SUBTRACTION 


33 


2.  Copy  the  following  table  and  show  («)  the  total  exports 
for  each  year  given ;  (5)  the  excess  of  exports  for  each  year 
given ;  (c)  the  total  exports  and  imports  for  the  ten  years ; 
(d)  the  total  excess  of  exports  for  the  ten  years.     Check. 

Imports  and  Exports  in  the  United  States  for  Ten  Years 


Year  End- 

Exports 

Total 
Exports 

Imports 

Excess  of 

ing  June  30 

Domestic 

Foreign 

Exports 

1904 

$1435179  017 

125  648  254 

$991090  978 

1905 

1  491  744  641 

26  817  025 

1117  513  071 

1906 

1  717  953  382 

25  911  118 

1  226  562  446 

1907 

1  853  718  034 

27  133  044 

1  434  421  425 

1908 

1  834  786  357 

25  986  357 

1  194  341  792 

1909 

1  638  355  593 

24  655  511 

1  311  920  224 

1910 

1  710  083  998 

34  900  722 

1  556  947  430 

1911 

2  013  549  025 

35  771  174 

1  527  226  105 

1912 

2  170  319  828 

34  002  581 

1  653  264  934 

1913 

2  428  506  358 

37  377  791 

1  812  978  234 

Total 

Under  the  term  domestic  exports  are  included  exports  of  merchandise, 
the  growth,  produce,  or  manufacture  of  the  United  States ;  under  foreign 
exports  are  inchided  articles  of  merchandise  previously  imported  into  the 
United  States  and  subsequently  reexported.  Under  the  term  imports  are 
included  imports  of  all  merchandise  of  whatever  origin  received  into  the 
United  States. 

49.  The  common  method  of  making  change  is  to  add  to  the 
price  of  the  goods  purchased  a  sum  that  will  equal  the  amount 
offered  in  payment. 

Thus,  if  a  person  buys  groceries  amounting  to  74/  and  tenders  $1  in 
payment,  the  mental  process  of  the  clerk  in  making  the  change  is  as  follows: 
"  74)2^  +  1)2^  4-  25/  =  $1";  the  customer  should  receive  as  change  a  1-cent 
piece  and  a  quarter  of  a  dollar. 

Change  may  be  made  in  a  number  of  ways.  In  the  above  example  two 
dimes  and  a  5-cent  piece  might  be  given  instead  of  the  quarter  of  a  dollar. 
In  the  following  exercise  name  the  largest  coins  and  bills  that  could  be  used. 

ORAL  EXERCISE 

1.  Name  the  coins  and  the  amount  of  change  to  be  given 
from  SI  for  each  of  the  following  purchases:  17/;  24/;  31/; 
38/;  45/;   52/;   59/;   m^;   73/;   80/;   87/;  18/;   25/. 


34 


PRACTICAL   BUSINESS   ARITHMETIC 


2.    Name  the  coins  and  the  amount  of  change  to  be  given 
from  12  for  each  of  the  following  purchases:  f  1.19;  #1.26; 


11.61;    11.68; 
11.41;   11.48; 


11.75;    11.82; 
11.55;   11.62; 


11.33;  11.40;  $1.47;  11.54 

$1.89;  11.20;   11.27;   $1.34 
11.69;  11.76;  $1.83;  $1.90. 

3.  Name  the  bills  and  coins  and  the  amount  of  change  to  be 
given  from  $5  for  each  of   the  following   purchases:    $1.21; 

$1.28;  $1.35;  $1.42;  $2.22;  $2.29;  $2.36;  $4.43;  $3.49; 
$4.50;  $3.51;  $3.56;  $4.57;  $2.58;  $1.63;  $2.64;  $1.65; 
$1.70;  $2.71;  $3.72;   $2.77;   $3.84;   $1.91;   $2.85;   $2.92. 

4.  Name  the  bills  and  coins  and  the  amount  of  change  to  be 
given  from  $10  for  each  of  the  following  purchases:  $4.93; 
$3.86;  $7.70;  $2.44 
$3.31;  $8.38;  $2.45 
$3.87;  $2.88;  $7.81 
18.29;  $8.32;  $7.25 

50.  It  is  frequently  necessary  to  find  the  difference  between 
a  minuend  and  several  subtrahends.  If  the  "  making  change  " 
method  of  subtraction  is  employed,  the  operation  is  a  simple 
one. 

51.  Example.  From  a  farm  of  578  A.  I  sold  at  one  time  162 
A.,  at  another  98  A.,  and  at  another  121  A.  How  many  acres 
remained  unsold  ? 


$8.37. 

$5.30; 

$3.23. 

$5.17; 

$4.24; 

$6.52 

$4.59; 

$3.66 

$5.73; 

$4.80; 

$9.74 

$5.67; 

$3.60 

;   $4.53; 

$2.46; 

$2.18 

$7.49; 

$9.42 

$3.67; 

$1.93. 

Solution.  Arrange  the  iminbers  as  shown  in  the  margin. 
Eleven  (1  +  8  +  2)  and  seven  are  18  ;  write  7.  Three  (1  carried 
+  2),  eighteen  (3  +  9  +  6)  and  nine  are  twenty-seven;  write  9. 
Four  (2  carried  +1  H[-  1)  and  one  are  5  ;  write  1. 

Check.     197  +  121  +  98  +  162  =  578. 

WRITTEN  EXERCISE 


578  A. 
162  A. 


121 
197  A. 


Find  the  amount  each  person  has  remaining  on  deposit : 

1.  A.    Deposit,  $900;  checks,  $210,  $175,  $198. 

2.  B.    Deposit,  $875 ;  checks,  $157,  $218,  $157. 

3.  C.    Deposit,  $750;  checks,  $120,  $117,  $121,  $118. 

4.  D.    Deposit,  $960;  checks,  $128,  $109,  $118, $117. 


SUBTRACTION 


35 


5.  E.    Deposit,  1967;  checks,  1192,  |102,  |117,  |128,|146. 

6.  F.    Deposit,  1998;  checks,  1119,  $117, 1105, 1123,1173. 

Do  not  neglect  to  check  all  work.  The  bank  clerk  who  makes  an  error 
a  day  in  work  like  the  above,  and  who  fails  to  discover  and  correct  this 
error,  will  not  long  retain  his  position. 

7.  Copy  the  following,  supplying  the  missing  terms  and 
checking  the  results  : 

$148.90  -h  $149.75  +  $421.77  =    $???.?? 

118.60+     172.12+     ???.??=       ???.?? 

242.30+     ???.??+     210.96=       ???.?? 

???.??+     168.72+     130.41  =  ,     ???.?? 
$718.95  +  $698.75  +  $978.60=$?  ?  ?  ?.  ?  ? 

The  following  problem  shows  a  portion  of  a  bank  discount  register.  In 
the  first  column  are  recorded  the  amounts  of  several  notes  that  have  been  dis- 
counted ;  in  the  second,  the  discount  charges ;  and  in  the  third,  the  collection 
and  exchange  charges.  The  proceeds  of  any  note  is  the  difference  between 
the  amount  (face)  of  the  note  and  the  total  charges  upon  it. 

8.  Copy  and  complete  the  following  bank  record.  Check 
the  work,      (j  +  z  +  7i  should  equal  g.) 


Face  of  Paper 

DlSCOLNT 

Coll.  &,  Excn. 

Proceeds 

729 

14 

7 

29 

73 

a 

862 

29 

4 

31 

86 

h 

725 

74 

7 

26 

73 

c 

832 

16 

12 

48 

1 

26 

fl 

426 

19 

6 

39 

43 

e 

378 

36 

3 

78 

38 

f 

9 

k 

i 

J 

52.  The  complement  of  a  number  is  the  difference  between 
the  number  and  a  unit  of  the  next  higher  order. 

Thus,  2  is  the  complement  of  8,  23  is  the  complement  of  77,  and  152  is 
the  complement  of  848.  3  and  7,  24  and  76,  250  and  750,  are  complementary 
numbers.  Observe  that  when  two  numbers  of  more  than  one  figure  each  are 
complementary/,  the  sum  of  the.  units'  figure  is  10  and  the  sum  of  the  figures  in 
each  corresponding  higher  order  is  9. 


36  PEACTICAL   BUSINESS  ARITHMETIC 

53.  Since  numbers  are  read  from  left  to  right,  in  finding  the 
complement  of  a  number,  begin  at  the  left  to  subtract. 

54.  In  beginning  at  the  left  to  subtract  take  1  from  the 
highest  order  in  the  minuend  and  regard  the  other  orders  as 
9's,  except  the  last,  which  regard  as  10. 

55.  Example.  A  man  gave  a  100-dollar  bill  in  payment  for 
an  account  of  ^77.52.     How  much  change  should  he  receive  ? 

Solutions,  (a)  Begin  at  the  left.  7  from  9  leaves  2;  7  from  9  $100.00 
leaves  2  ;  5  from  9  leaves  4 ;  2  from  10  leaves  8.     Or  77  'i*'? 

(6)    7  and  2  are  9  ;  7  and  2  are  9  ;   6  and  4  are  9  ;   2  and  8  are  ^       '  /I 

10.     $22.48.  ^22AH 

This  method  of  finding  the  amount  of  change  is  used  by  many  clerks  and 
cashiers.  The  work  is  in  all  cases  proved  by  counting  out  to  the  customer 
the  bills  and  coins  necessary  to  make  the  amount  of  the  purchase  equal  to 
the  amount  offered  in  payment. 

ORAL  EXERCISE 

Find  the  total  of  each  group  of  numbers,  then  find  the  difference 
between  the  two  totals : 

1.  (24  26  32  30  35  25)  -  (18  13  19  12  20  30). 

2.  (13  27  45  25  21  19)-  (15  14  21  32  18  22). 

3.  (11  29  35  15  24  16)  -  (27  13  18  22  25  20). 

4.  (17  14  29  32  22  26)  -  (23  13  16  24  20  16). 

5.  (45  25  30  40  32  18)  -  (25  35  33  17  20  3t)). 

6.  (34  24  35  30  15  32)  -  (21  39  14  15  11  30). 

7.  (15  25  33  27  14  36)  -  (13  30  16  14  20  16). 

8.  (14  16  30  10  40  50)  -  (11  19  18  12  20  30). 

9.  (19  10  11  20  30  32)  -  (15  11  14  30  32  18). 

10.  (33  17  22  11  17  50)  -  (21  19  31  12  17  40). 

11.  (25  30  15  40  15  20)  -  (15  16  19  21  29  30). 

12.  (17  23  25  26  15  44)  -  (24  20  26  27  13  20). 

13.  (11  39  52  18  10  20)  -  (12  18  40  22  28  12). 

14.  (35  15  27  23  34  16)  -  (21  17  12  42  13  15). 

15.  (22  18  34  26  60  10)  -  (35  15  20  11  19  31). 

16.  (33  17  22  18  40  60)  -  (14  26  23  17  40  12). 


SUBTKACTION 

37 

ORAL  EXERCISE 

State  the  amount 

of  change  in 

each  of  the  following  problems  : 

Cost  of 

Amount 

Cost  of 

Amount 

Items  Purchased 

Paid 

Items  Purchased 

Paid 

1. 

17^,  13^,  42^ 

$2 

14. 

$1.25,    $0.75,12.18 

$20 

2. 

27^,  23^,  14^ 

$2 

15. 

11.50,    12.70,11.18 

$20 

3. 

45^,  55^,  13^ 

15 

16. 

$4.60,    $1.40,  $2.13 

$20 

4. 

64^,  16^,  87^ 

$5 

17. 

$1.50,    $1.20,  $2.30 

$10 

5. 

23^,  14^,  27^ 

$2 

18. 

$3.17,    $4.11,  $4.98 

$50 

6. 

63. <  17^,  59 P 

15 

19. 

$4.25,    $0.75,  $3.18 

$20 

7. 

49^,  84^,  37^ 

15 

20. 

$1.29,    $2.17,11.50 

$20 

8. 

78^,  42^,  67^ 

15 

21. 

$1.64,    $1.66,  $2.50 

$20 

9. 

52^,  69^,  88^ 

15 

22. 

$1.59,  $23.41,   $118 

$200 

10. 

75^,  86^,  54^ 

15 

23. 

$24.17,  $20.83,     $15 

$100 

11. 

89^,  46^,  72)^ 

f5 

24. 

$11.48,  $10.52,     $50 

$100 

12. 

76^,  54^,  29^ 

15. 

25. 

$18.91,  $12.09,     $45 

$100 

13. 

75^,  25^,  89^ 

810 

26. 

$21.27,  $2.73,  $50.50 

$100 

56.  19  —  7  =  9  (the  minuend  minus  10)  +  3  (the  comple- 
ment of  tlie  subtrahend);  191  —  17  =  91  (the  minuend  minus 
100)  +  83  (the  complement  of  the  subtrahend)  ;  1912  -  178  = 
912  (the  minuend  minus  1000)  +  822  (the  complement  of  the 
subtrahend),  and  so  on. 

57.  This  principle  makes  it  a  simple  matter  to  find  the  dif- 
ference between  a  subtrahend  and  several  minuends. 

58.  Examples.  The  following  examples  illustrate  the  appli- 
cation of  the  principle: 

Solutions.  1.  2  (the  complement  of  8), 
10,  16;  16-10  =  6.  9  (the  complement  of  1), 
16,  17;  17-10  =  7.     9,  13,  16;  16-10=6. 

2.  9,  17,  26;  26-10  =  16;  that  is,  6  and  1 
to  add  to  the  minuends.  9,  18  (9  +  8  +  1),  27;  —118  —111  —219 
27-10  =  17;  that  is,  7  and  1  to  add  to  the  =676  =676  =203 
minuends.     9,  14,  16;  16-10  =  6. 

3.  1,  2,  3.  3  —  10  is  impossible,  so  subtract  1  ten  from  the  minuend  (or  add 
1  ten  to  the  subtrahend).     9,  10.     10-10  =  0.     8,  9,  12.     12-10  =  2. 


1. 

2. 

3. 

316 

299 

311 

+  478 

4-488 

+  111 

38 


PRACTICAL   BUSINESS   ARITHMETIC 


59.   Example.    The  following  problem  shows  a  concrete  appli- 
cation of  the  foregoing  principle  ; 

Depositors'  Ledger 


Solution,  Here  is  a 
depositors'  ledger.  The 
data  in  the  first  three 
columns  being  given,  it 
is  required  to  find  the 
new  balance. 

The  process  is  as  follows:    A.  6,  11,  15,  5;   8,  16,  23,  13;  balance,  $1.35. 

B.  9,  18,  24,  4  and  1  to  add  to  the  minuend.     10,   19,  27,  17;  balance,  $174. 

C.  1,  2,  4  and  1  to  take  away  from  the  minuend.     7,  10,  19,  9;  balance,  f  94. 


Depositor 

Balance 

Checks 

Deposits 

Balance 

A 
B 
C 

174 
186 
$92 

$25 
$  11 

$79 

$86 
$99 

$81 

$135 
$174 
$    94 

WRITTEN  EXERCISE 

Find  the  new  balances^  the  total  old  balance^  the  total  checks^  the 
total  deposits^  the  total  new  balances^  and  check  the  work: 

1.  2. 


Depositor 

Bal. 

Checks 

Deposits 

Bax. 

A 

$758 

$128 

$  421 

a 

B 

921 

154 

175 

h 

C 

934 

214 

122 

c 

D 

862 

162 

218 

d 

E 

478 

187 

126 

e 

F 

921 

215 

124 

f 

G 

756 

157 

137 

r/ 

H 

864 

128 

142 

h 

I 

926 

214 

121 

i 

J 

752 

221 

124 

J 

K 

878 

162 

218 

k 

/ 

m 

n 

0 

Depositor 

Bal. 

Checks 

Deposits 

Bal. 

A 

$428 

$125 

$  718 

a 

B 

726 

128 

296 

b 

C 

832 

279 

318 

c 

D 

456 

154 

421 

d 

E 

298 

275 

568 

e 

F 

728 

178 

188 

f 

G 

762 

218 

215 

9 

H 

837 

316 

176 

h 

I 

493 

121 

219 

i 

J 

862 

128 

188 

J 

K 

925 

125 

211 

k 

/ 

7)1 

n 

0 

60.  48  -  29  =  48  +  1  (30,  the  next  higher  order  of  units  than 
29,  -  29)  -  30,  or  19  ;  128  -59=  128  +  1  -  60,  or  69. 

61.  This  principle  may  be  applied  to  advantage  in  billing 
items  in  which  the  gross  weights  and  the  tares  are  recorded. 

The  gross  weight  is  the  weight  of  merchandise,  together  with  bag,  cask, 
or  other  covering ;  the  tare  is  the  weight  of  the  bag,  cask,  or  other  covering 


SUBTRACTION 


39 


of  merchandise ;  the  net  weight  is  the  difference  between  the  gross  weight 
and  the  tare. 

62.  Example.  The  gross  weights  and  tares,  in  pounds,  of  3 
bbl.  of  sugar  are:  332  -  19,  337  -  18  335  -  18.  Find  the  total 
net  weight. 

jrr;eTHuero„rim  332-19  337 -is  335 -is  949# 

horizontally,  as  shown  in  the  margin.  Adding  the  units  of  the  tare,  the  result 
is  25  ;  30  (the  next  higher  order  of  units  than  25)  minus  25  equals  5  ;  5  added 
to  the  units  of  the  gross  weight  equals  19 ;  19  —  30  is  impossible,  so  write  9 
and  subtract  2  tens  (the  difference  between  the  tens  in  30  and  19)  from  the 
gross  weight  or  add  2  tens  to  the  tens  of  the  tare.  Adding  2  tens  to  the  tens 
of  the  tare,  the  result  is  5  ;  10  —  5  =  5  ;  5  added  to  the  tens  of  the  gross  weight 
equals  14  ;  14  —  10  =  4.  Adding  the  hundreds  in  the  gross  weight,  the  result 
is  9.    Net  weight  is  949  lb. 

WRITTEN   EXERCISE 

Copy  the  following  hills.  Verify  the  net  weights  given  and  sup- 
ply all  missing  terms. 

1. 


M/'^,^^^,^^ 


Chicago.  III.. 


t^^^/^ 


'^/^^ 


-=^^<^^ 


c^.^^^^/  Z-f 


-19- 


^-^■^^.^■'f::^^^^-. 


=i£^S 


:^^^ 


Bought  of  PHILIP  ARMOUR  &  CO. 


Terms- 


^^!^.^^^^.-^7^^^^-g7^ 


y^  -  /^A 


/^  -VZ-Z^T 


//^-r        ^-3? 


J^ 


^ 


^^^r:? 


k^ 


'C'C^'fi^ 


O'^^^ 


4^^^-^^    4^^-^-7^     ^z-^x-yn       2-/z^/ 'Jt 


Z^ 


7^ 


.^ 


.--r^-rPL 


\..4^^^  ry>/-r:7^^^-^  ^^ 


^zff-70      ^//-7o 

^ai'-yo       i/i/2--'y/       4^/(^-1^^ 


/£>    3 


^ 


2A 


ik*^ 


40 


PEACTICAL   BUSINESS   ARITHMETIC 


Chicago,  IIL,       July  20,       J9 

Messrs.   A.   M.    THOMPSON  &  CO. 

Rochester,    N.Y. 

Botj§:ht  of  Nelson,  Morris  &  Co^ 

Terms  30  da. 


tubs  Lard 
72-17  70-14 
69-14  71-14 
71-15  70-16      ***    $0.13 

casks  Shoulders 
421-65  426-70 
424-72  422-64 
427-72  421-60   ####    .14 

casks  Hams 

409-72  412-70 
414-71  410-73 
412-70  416-71   **#*    .18 


43 


299 


368 


29 


32 


28 


3.  The  gross  weights  and  tares  of  6  casks  of  shoulders  are 
as  follows  :  428  -  68,  419  -  70,  423  -  65,  432  -  72,  436  -  69, 
434  —  65  lb.     Find  the  total  net  weight. 

4.  The  gross  weight  and  tares  of  12  tubs  of  lard  are  as  fol- 
lows :  71-14,  70-15,  69-14,  71-15,  72-17,,  73-17, 
69  -  15,  71  -  16,  72  -  15,  73  -  16,  74  -  17,  75  -  17  lb.  Find 
the  total  net  weight. 

5.  The  gross  weights  and  tares  of  10  bbl.  of  sugar  are  as 
follows:  319-18,  331-19,  329-17,  334-20,  338-21, 
325  -  18,  326  -  16,  325  -  19,  327  -  19,  321  -  17  lb.  Find  the 
total  net  weight. 


SUBTEACTION 


41 


BUSINESS   TERMS   AND   EECOEDS 

63.  A  debit  is  an  expression  of  value  received ;  a  credit  is 
an  expression  of  value  delivered. 

A  buys  of  B  100  bu.  wheat  for  $100  cash;  the  vahie  received  (debit) 
by  A  is  100  bu.  wheat  and  the  value  parted  with  (credit),  §100.  A  sells  C 
50  bu.  wheat  for  $75,  C  agreeing  to  pay  for  the  same  in  10  da. ;  the  value 
received  by  A  is  C"s  express  or  implied  promise  to  pay  for  the  wheat  in  10  da. 
and  the  value  parted  with  is  50  bu.  wheat. 

64.  An  account  is  a  collection  of  related  debits  and  credits. 

65.  Some  of  the  common  accounts  kept  in  business  are  the  cash 
account;  personal  accounts;  the  merchandise  account;  the 
expense  account ;  the  proprietary  account. 

66.  A  resource  is  any  property  on  hand  or  any  amount  owed 
to  a  person  or  concern;  a  liability  is  any  amount  owed  by  a 
person  or  concern.  The  excess  of  resources  over  liabilities  is 
the  net  capital  or  present  worth ;  the  excess  of  liabilities  over 
resources,  the  net  insolvency. 

67.  A  gain  is  any  sum  realized  in  excess  of  the  cost  of  a 
business  or  of  business  transactions ;  a  loss  is  any  sum  spent 
or  incurred  in  excess  of  the  returns  of  a  business  or  of  business 
transactions.  The  excess  of  gains  over  losses  is  the  net  gain ; 
the  excess  of  losses  over  gains,  the  net  loss. 

68.  The  cash  account  is  kept  for  the  purpose  of  showing  the 
receipts  and  payments  of  cash  and  the  amount  of  cash  on  hand. 


f 


/2 


/JA^-J^ 


/Z(P0 


/A^¥^\J'a 


The  receipts  are  entered  on  the  left,  or  debit  side,  the  payments,  on  the 
right,  or  credit  side.    The  excess  of  debits  is  the  balance  or  cash  on  hand. 
In  these  exercises  the  use  of  red  ink  is  not  imperative. 


42 


PEACTICAL   BUSINESS  ARITHMETIC 


69.  Personal  accounts  are  kept  for  the  purpose  of  showing 
whether  persons  owe  us  or  w§  owe  them,  and  how  much  in 
either  case. 


On  the  left  (debit)  side  of  these  accounts  are  placed  the  amounts  which 
the  persons  owe  us  or  which  we  j)ay  them  ;  on  the  right  (credit)  side,  the 
amounts  which  we  owe  them  or  which  they  pay  us.  Wlien  the  debits 
of  an  account  are  in  excess  of  the  credits,  the  account  owes  us  for  the  amount 
of  the  excess;  when  the  credits  are  in  excess  of  the  debits,  we  owe  the  ac- 
count for  the  amount  of  the  excess. 

70.  The  merchandise  account  is  kept  for  the  purpose  of  show- 
ing the  cost  of  goods  purchased,  the  proceeds  of  goods  sold,  and 
the  gain  or  loss  resulting  from  such  dealings. 


y/^^64.^^izJ^-^:L<n.^^ 


/z 


^l^ 


/r  -*^?^^2z,ii^^?^^ 


/  6o 
27s 


22.7^ 


^36^ 


7^ 


Cs 


Co 


6^rz...^>ff-Ccf  firs>-z^ 


t/3£P  6  a' 
J  ^o  /J- 


JLZA 


^ 


On  the  left  (debit)  side  is  entered  the  cost  of  goods  purchased  and  on  the 
right  (credit)  side  the  proceeds  of  goods  sold.  When  the  goods  are  all 
disposed  of  the  excess  of  credits  is  a  gain  ;  the  excess  of  debits,  a  loss. 
When  it  is  desired  to  show  the  gain  or  loss  on  merchandise  before  the 
goods  are  all  disposed  of,  it  is  necessary  to  first  enter  in  the  credit  side  of 
the  account  the  present  market  value  of  the  unsold  goods. 


SUBTRACTION 


43 


71.    The  expense  account  is  kept  for  the  purpose  of  showing 
the  cost  of  outlays  incurred  in  carrying  on   the  business. 


C^. 


SH^CV^n,^ 


/^ 


/  2 


JT^ 


£zk£ 


^a 


Such  outlays  are  entered  on  the  left  (debit)  side  of  the  account.  Ordi- 
narily there  are  no  credit  entries.  When  the  expense  items  are  all  used  the 
debit  of  the  account  is  a  loss.  When  it  is  desired  to  show  the  loss  or  gain 
on  expense  and  there  are  unused  expense  items  on  hand,  it  is  first  necessary 
to  enter  in  the  credit  side  of  the  account  the  present  value  of  such  items. 

72.  The  proprietary  account  is  kept  for  the  purpose  of  show- 
ing how  much  the  proprietor  invests  in  the  business  and  how 
much  he  withdraws  from  the  business. 


:^^Jr:^^i:^^ 


/o 


'■^u^yy^^r-^^ 


/Co  — 


ijJs^ 


^f  f^ 


On  the  right  (credit)  side  are  entered  all  sums  invested  and  the  net  gain, 
and  on  the  left  (debit)  side  all  sums  withdrawn  and  the  net  loss.  The 
excess  of  credits  is  the  present  worth  of  the  business. 

ORAL  EXERCISE 

1.  In  the  cash  account  on  page  41  what  are  the  total  receipts? 
the  total  payments  ?  the  balance  of  cash  on  hand  ? 

2.  At  the  top  of  page  42  is  your  account  with  J.  E. 
King  &  Co.  On  what  dates  did  you  sell  the  firm  merchandise  ? 
When  and  how  were  payments  made  on  account?  What  was 
the  balance  of  the  account  May  10  ? 


44  PRACTICAL   BUSINESS   ARITHMETIC  . 

3.  In  the  account  with  merchandise,  page  42,  what  is  the 
cost  of  the  purchases?  the  proceeds  of  the  sales?  How  would 
the  value  of  the  unsold  goods  be  determined  in  business  ? 
Verify  the  amount  of  the  gain.     Is  it  correct  ? 

4.  Verify  the  amount  of  the  loss  in  the  expense  account, 
page  43.     Is  it  correct  ? 

5.  What  are  the  total  withdrawals  in  the  account  with 
F.  W.   Simpson,  Proprietor,  page   43  ?  the  total  investment  ? 

WRITTEN    EXERCISE 

1.  Copy  the  cash  account  on  page  41  and  continue  it  with 
the  following  items:  Jan.  12,  receive  cash  of  Jones  &  Co., 
175;  Jan.  14,  pay  cash  for  groceries,  $165.62;  Jan.  15,  re- 
ceive cash  for  groceries,  $  189.75  ;  Jan.  18,  pay  cash  to  office 
help,  $129.74;  Jan.  20,  pay  cash  for  stationery,  $11.75; 
Jan.  22,  receive  cash  for  groceries,  $126.94;  Jan.  24,  receive 
cash  of  H.  W.  Conant,  $200.67.  Balance  the  account  as  shown 
in  the   model. 

2.  Copy  the  purchases  and  sales  of  the  merchandise  account, 
page  42.  Assuming  that  the  value  of  the  unsold  goods  is 
$327.61,  find  the  gain  and  close  the  account. 

3.  Copy  the  purchases  and  sales  of  the  merchandise  account, 
page  42.  Assuming  that  the  value  of  the  unsold  goods  is  $50, 
find  the  gain  or  loss  and  close  the  account.  Assuming  that  all 
of  the  goods  are  sold,  find  the  gain  or  loss  and  close  the  account. 

4.  Arrange  the  following  data  in  the  form  of  your  account 
with  Benj.  F.  Butler.  June  1,  buy  of  Benj.  F.  Butler  on 
account  (without  making  payment)  dry  goods  amounting  to 
$627.96;  June  10,  pay  him  for  invoice  of  June  1  less  $6.28 
discount;  June  28,  buy  of  him  dry  goods  amounting  to  $472.69 
and  pay  cash  to  apply  on  the  bill,  $172.69;  July  15,  buy  of  him 
on  account  dry  goods  amounting  to  $369.71;  July  31,  pay  him 
cash  to  apply  on  bill  of  July  15,  $79.79;  Aug.  2,  sell  him  lace 
amounting  to  $14.60.  Find  the  balance  of  the  account  and 
tell  whether  such  balance  is  a  resource  or  a  liability. 


SUBTRACTION 


45 


5.  Using  the  above  data,  write  Benj.  F.  Butler's  account  of 
his  dealings  with  you.     Balance  the  account. 

6.  Copy  the  account  with  F.  W.  Simpson,  Prop.,  page  43. 
Continue  the  account  through  June,  using  the  following  items : 
June  6,  make  an  additional  investment  of  flOOO;  June  25, 
withdraw  for  personal  use  |160;  June  30,  the  net  gain  for  the 
month,  which  is  to  remain  as  an  additional  investment,  is 
$369.75.     Find  the  present  worth  and  close  the  account. 

WRITTEN   EXERCISE 


Copy  the  following  statements^  supplying  the  missing  terms  : 


x:^^iz^^^^^<^<n^^y^^2^a/<=^^^^ 


J/,/f-^ 


Qy:^::j^h.e^^yL.J..^^ 


J^;^ 


3ZO0 


CC! 


■"'  .'  .' 


■fZ 


2. 


x:y^^Z'^^^>^^i-^'^z^^/^^^ 


^^n^7;^t<J/^ 


Co 


J  o  o 

F  .-'  '' 


/j^j\Co 


46  PRACTICAL   BUSHSTESS   ARITHMETIC 

3.  A  merchant  purchased  a  stock  of  hardware  amounting  to 
i45,112.18  and  sold  from  this  stock  goods  amounting  to 
$31,136.85.  He  then  took  an  account  of  stock  and  found  that 
the  value  of  the  hardware  on  hand  was  $18,438.50.  Find  the 
amount  of  his  gain. 

4.  C.  E.  Cyr's  resources  and  liabilities  at  the  close  of  a 
month  were  as  follows:  dry  goods  on  hand,  $1629.40;  store 
and  lot,  $3000;  cash  in  bank,  $1400.60;  C.  O.  Bond  owes  the 
business  $400;  L.  E.  Young,  $390.10;  and  J.  O.  Snow, 
$209.90.  The  business  owes  Roe  &  Co.  $750;  and  Doe  &  Co. 
$90.75.     Make  a  statement  of  resources  and  liabilities. 

5.  At  the  close  of  the  same  month  C.  E.  Cyr's  business 
accounts  show  the  following  results:  stock  of  dry  goods  on 
hand  at  the  beginning  of  the  month,  $1270.40;  purchases  of 
dry  goods  for  the  month,  $3229.60;  sales  of  dry  goods  for  the 
month,  $3762.90;  market  value  of  the  dry  goods  on  hand  at 
the  close  of  the  month,  $1629.40;  expense  for  the  month, 
$413.95;  value  of  expense  items  on  hand,  $250.  Make  a  state- 
ment of  losses  and  gains. 

6.  A  real  estate  agent  had  property  on  hand  Jan.  1  to 
the  amount  of  $8155.60.  During  the  year  he  bought  property 
costing  S  4150.60,  added  buildings  at  a  cost  of  S  6190.40,  and 
paid  in  taxes  S  250.90.  April  15  a  house  valued  at  S1690  was 
destroyed  by  fire,  and  for  this  loss  the  insurance  company  paid 
him  $1300.  During  the  year  he  sold  property  for  S  9260.50  and 
received  for  rents  S  840.80.  If  the  expenses  of  the  sales  aggre- 
gated $240.19,  and  the  value  of  the  property  on  hand  Dec.  31 
was  $11,250.60,  what  was  his  net  gain  or  loss  for  the  year? 

7.  A  real  estate  agent  bought  a  piece  of  land  for  $6254.25. 
He  made  the  following  expenditures:  for  grading,  $328.65;  for 
draining,  $28.30;  for  taxes,  $98.45;  for  the  construction  of  a 
dwelling  house,  $4580.  In  the  course  of  the  year  he  sold  a  house 
and  lot  for  $6685.40  ;  5  lots  for  $845.25  each.  If  his  expenses 
including  insurance  were  $175.50,  and  he  still  owned  2  lots 
valued  at  $950  each,  what  was  his  gain  on  the  whole  transaction? 


SUBTRACTION 


47 


WRITTEN   EXERCISE 

Copy  each  of  the  folloiving  examples;  complete  the  work^  arid 

check  the  result.    Time^   approximately^    thirty  minutes.    Face   of 

paper ^  minus  discount  and  collection  and  exchange^  equals  proceeds. 

Face  OF  Paper 

1.  $376.25 
255.78 
176.44 
259.86 
492.71 
149.52 
643.15 
319.21 


? 

Face  of  Paper 

2.  S  186.73 
237.50 
412.88 
337.95 
360.90 
245.91 
307.55 
250.40 


3. 


Face  of  Paper 

S421.95 
112.70 
324.50 
245.60 
194.75 
217.50 
311.59 
289.72 


Discount 

Coll.  and  Exch. 

Proceeds 

S3.76 

$0.38 

9 

1.28 

0.26 

9 

1.76 

9 

2.60 

0.26 

? 

2.46 

0.49 

9    . 

0.75 

0.15 

? 

6.43 

0.64- 

9 

0.80 

? 

9 

? 

9 

Discount 

Coll.  and  Exch. 

Proceeds 

$1.87 

•       $0.19 

9 

2.38 

0.24 

9. 

4.13 

? 

3.38 

0.34 

? 

0.90 

? 

1.23 

0.25 

9 

3.08 

0.31 

9 

3.76 

0.25 

9 

9 

? 

9 

Discount 

Coll.  and  Exch. 

Proceeds 

$2.11 

$0.42 

9 

1.13 

0.11 

9 

1.62 

9 

2.46 

0.25 

9 

0.92 

0.19 

9 

1.09 

0.22 

9 

3.12 

0.31 

9 

1.45 

0.29 

9 

9 

9 

9 

48 


PRACTICAL   BUSINESS  ARITHMETIC 


WRITTEN    EXERCISE 


Copy  each  of  the  following  examples  ;  find  the  new  balance^  the  total 
old  balance,  the  total  checks,  the  total  deposits,  and  check  the  work : 


Name     Bal.   Checks  Deposits  Bal. 


2. 

Name     Bal.  Checks  Deposits  Bal. 


A 

S516 

S423 

$313 

? 

A 

$309 

$423 

$267 

? 

B 

203 

507 

398 

? 

B 

476 

379 

112 

? 

C 

195 

461 

412 

? 

C 

277 

407 

321 

? 

D 

204 

165 

? 

D 

255 

126 

? 

E 

335 

515 

296 

? 

E 

167 

217 

178 

? 

F 

411 

309 

156 

? 

F 

213 

453 

329 

? 

G 

135 

257 

145 

? 

G 

208 

196 

114 

? 

H 

295 

512 

? 

H 

126 

240 

114 

? 

I 

500 

316 

104 

? 

I 

255 

153 

? 

J 

450 

225 

117 

? 

J 



212 

317 

? 

K 

650 

751 

211 

? 

K 

455 

235 

103 

? 

L 

512 

337 

206 

?' 

L 

275 

230 

115 

? 

M 

242 

176 

105 

? 

M 

315 

275 

144 

? 

? 

? 

3. 

? 

? 

? 

9 
4. 

? 

? 

^AME 

:  Bal. 

Checks  Deposits 

Bal. 

Name 

;  Bal. 

Checks  Deposits  Bal, 

A' 

S311 

S242 

S301 

? 

A 

$267 

$133 

$145 

9 

B 

23i5 

115 

118 

? 

B 

247 

315 

9 

C 

178 



212 

? 

C 

256 

119 

228 

9 

D 

142 

188 

206 

? 

D 

116 

177 

9 

E 

268 

315 

? 

E 

215 

411 

196 

9 

F 

447 

397 

109 

? 

F 

423 

375 

116 

9 

G 

214 

375 

226 

? 

G 

198 

213 

132 

9 

H 

154 

106 

? 

H 

245 

157 

109 

9 

I 

256 

400 

144 

? 

I 

233 

334 

168 

9 

J 

512 

613 

199 

? 

J 

443 

337 

155 

9 

K 

245 

237 

155 

? 

K 

704 

856 

266 

9 

L 

146 

114 

9 

L 

231 

250 

119 

9 

M 

565 

743 

248 

? 

M 

178 

252 

107 

? 

? 

? 

? 

? 

? 

? 

? 

? 

SUBTRACTION  49 


A   WRITTEN   REVIEW   TEST 

Write  problems  1  and  2  from  dictation^  and  then  complete  the 
work.    Time,  approximately,  forty  nmmtes,  including  the  dictation. 


1.    Add  the  following  and  check  the  results 


3412 

4571                           3582 

? 

6243 

8132                            2738 

? 

1729 

2642                            9810 

? 

4572 

7235                           1345 

? 

2643 

6254                           4165 

? 

3414 

8149                            3542 

? 

7145 

6127                           4713 

? 

3328 

2170                           2312 

?  . 

5331 

4262                           1745 

? 

3473 

1208                            8052 

? 

? 

?                                  ? 

? 

2.    Find 

the  new  balance,  the  total  old  balance. 

the   total 

checks,  the  total  deposits,  and  check  the  work : 

Name 

Balance                    Checks                  Deposits 

Balance 

A 

$235                $142                 $217 

? 

B 

312                   254                    122 

? 

C 

288                    300                    212 

? 

D 

542                   250                    106 

? 

E 

350                    500 

? 

F 

•  600                   325                   

? 

G 

750                                           252 

? 

H 

219                   200                    151 

? 

I 

224                   100                    216 

? 

J 

116                   330                   214 

? 

K 

255                   225                   110 

? 

? 

?                        ?                       ? 

? 

3.  The  text,  page  46,  problem  3. 

4.  The  text,  page  46,  problem  6. 

5.  The  text,  page  46,  problem  7. 


CHAPTER   VI 

MULTIPLICATION 
ORAL   EXERCISE 

1.  Which  of  the  following  numbers  are  concrete  ;  that  is,  re- 
fer to  some  particular  kind  of  object  or  measure?  12  ;  5J  ;  12 
ft.  ;   2.5  da.  ;  15  yd.  ;   18  men  ;   200;   ef  12  ;   172f 

2.  Which  of  the  above  numbers  are  abstract ;  that  is,  do  not 
refer  to  any  particular  kind  of  object  or  measure  ? 

3.  5  +  4  +  2  +  8  4-9  =  ? 

4.  9  +  9  +  9  +  9  +  9=?   5  times  9  =  ? 

5.  Could  the  sum  of  the  numbers  in  problem  3  be  found  by 
any  shorter  process? 

6.  What  is  the  first  process  in  problem  4  called  ?   the  second? 

7.  9  times  27  =  ?     9  times  29  bu.  =  ? 

8.  If  1  bu.  of  rye  weighs  56  lb.,  what  will  12  bu.  weigh? 

73.  In  problems  7  and  8  it  is  seen  that  the  multiplier  is 
always  an  abstract  number  ;  and  the  multiplicand  and  product  are 
like  numbers. 

74.  Three  5's  are  equal  to  five  3's  ;  $3  multiplied  b}^  5  is 
equal  to  15  multiplied  by  3  ;  4  trees  multiplied  by  125  is  equal 
to  125  trees  multiplied  by  4. 

75..  It  is  therefore  seen  that  the  product  is  hot  affected  by 
changing  the  order  of  the  factors  regarded  as  abstract  7iumbers. 

76.  The  multiplicand  and  multiplier  together  are  called 
factors  (makers)  of  the  product  ;  the  product  of  two  abstract 
integers  is  sometimes  called  a  multiple  of  either  of  the  factors. 

77.  Sometimes  a  number  is  used  several  times  as  a  factor. 
Numbers  so  used  are  indicated  by  a  small  figure,  called  an  expo- 
nent, written  above  and  at  the  right  of  the  factor. 

Thus,  4  used  twice  as  a  factor  is  written  4^,  5  used  four  times  as  a  factor 
is  written  5*,  and  6  used^'ye  times  as  a  factor  is  written  6^. 

50 


MULTIPLICATION  51 

78.  The  product  arising  from  using  a  number  two  or  more 
times  as  a  factor  is  called  a  power  of  that  number. 

Thus,  4  is  the  second  power  of  2  ;  64  is  the  third  power  of  4  and  the  sixth 
power  of  2. 

Too  much  attention  should  not  be  given  to  the  definitions  like  the  above. 
They  are  valuable  only  as  they  help  to  make  clear  the  matter  in  the  exercises. 
They  are  rarely  heard  in  business  and  therefore  should  not  be  memorized. 

ORAL  EXERCISE 

1.  Multiply  at  sight  each  number  below  by  2  ;  by  3 ;  by  4  ; 
by  5;  by  6;  by  7;   by  8 ;  by  9. 

Name  the  products  by  lines  from  left  to  right  and  from  right  to  left; 
also  by  columns  from  left  to  right  and  from  right  to  left.  Name  results 
only.  Thus,  to  multiply  lines  by  4  say  20,  36,  8,  24,  40,  12,  28,  44,  16,  48, 
32,  52,  68, 84,  and  so  on  up  to  100 ;  and  backwards,  100,  80,  96,  64,  and  so  on 
back  to  20.  To  multiply  columns  by  4  say  20,  68,  36,  84,  and  so  on  to  52, 
100 ;  and  backwards  100,  52,  80,  32,  and  so  on  to  68,  20.  Continue  the  work 
until  results  can  be  named  at  the  rate  of  120  or  more  per  minute. 

5        9       2       6       10       3       7       11       4       12       8       13 
17       21     14     18       22     15     19       23     16       24     20      25 

2.  Multiply  as  instructed  in  problem  1  and  add  8  (carried) 
to  each  product.  Also  multiply  as  instructed  and  add  6,  4,  7, 
2,  5,  3,  and  9  to  each  product. 

Name  results  only.  Thus,  to  multiply  by  lines  say  20,28;  36,  44;  8, 
16;  and  so  on. 

3.  Multiply  by  2  :  27,  35,  81,  36,  28,  32,  47,  93,  56,  39,  54, 
45,  52,  86,  75,  67,  59.     Also  by  4,  3,  5,  8,  6,  7,  9. 

4.  Find  the  cost  of  each  of  the  following:  20  lb.  crackers  at 
8^;  9  lb.  coffee  at  34^;  7  lb.  tea  at  57^;  11  lb.  beef  at  17^; 
120  lb.  sugar  at  4^;  134  lb.  sugar  at  5^. 

5.  Find  the  cost  of  each  of  the  following:  44  yd.  at  9^;  37 
yd.  at  8^;  123  yd.  at  6^;  214  yd.  at  4^;  52  yd.  at  12^;  29 
yd.  at  8^;  8  yd.  at  11.03;  7  yd.  at  il. 01;  5  yd.  at  11.35. 

6.  Beginning  at  0  count  by  9's  to  81 ;  by  lO's  to  150 ;  by  ll's 
to  154;  by  12's  to  108;  by  13's  to  117;  by  14's  to  126;  by 
15's  to  135;  by  16's  to  144;  by  17's  to  153 ;  by  18's  to  162;  by 
19's  tol71;  by  20'stol80. 


52  PRACTICAL   BUSINESS   ARITHMETIC 

79.    Examples,    i.  Find  the  cost  of  2150  lb.  at  5^. 

Solution.     Since  1  lb.  costs  hf,  2150  lb.  will  cost  2150  times      $  21.50 
5^;  but  2150  times  hf    is  equal  to  5  times   2150^.    5    times  5 

$21.50  (2150 i?)  equals  $107.50,  the  required  result.  ^5  ^07. 50 

2.  Multiply  224  by  46. 

Solution.     In  multiplying  one  number  by  another,  224             224 

there  is  no  practical  advantage  in  beginning  with  the  4g               46 

lowest  order  of  units  of  the  multiplier ;   in  fact,  in  -j  0  ,  <           896~ 

some  multiplications  there  is  a  decided   advantage  ^.q^             -.  o  1  i 

in  beginning  with  the  highest  order.    The  arrange- • 

ment  of  work  for  both  methods  is  shown  in  the  lUoU4  lUoU-4 
margin. 

Check.     The  work  may  be  checked  by  multiplying  first  by  one  method  and 

then  by  the  other,  or  by  interchanging  the  multiplier  and  multiplicand  and  re- 
multiplying.     (See  also  pages  89  and  90.) 

3.  Multiply  2004  by  1275. 

Solution.     When  one  of  two  numbers  to  be  mul-              1275  1275 

tiplied  contains  a  number  of  zeros  or  ones,  it  is  always              2004  2004 

easier  to  take  that  number  as  the  multiplier.     Since              VhTo  ^^^^0 

the  product  of  any  number  multiplied  by  0  is  0,  the  qptca  ^      f^inn 

product  of  1275  multiplied  by  the  tens  and  hundreds  — '^^ 

of  the  multiplier  need  not  be  written.  2o5d100  2o55100 

Check.    The  problem  may  be  checked  the  same  as  problem  2. 

When  two  numbers  are  to  be  multiplied,  it  is  generally  easier  to  take  as 
the  multiplier  the  number  having  the  least  number  of  places.  Thus,  to  find 
the  cost  of  1647  A.  of  land  at  $27  per  acre,  take  27  as  the  multiplier. 

If  one  of  the  two  numbers  to  be  multiplied  has  two  or  more  digits  alike, 
it  is  easier  to  take  that  number  as  the  multiplier.  Thus,  to  multiply  to- 
gether 6729  and  7777,  it  is  easier  to  take  7777  as  the  multiplier. 


ORAL    EXERCISE 

1.  Find  the  value  of  51  T.  of  hay  at  $17  per  ton. 

2.  Find  the  cost  of  175  lb.  of  sugar  at  5^  per  pound. 

3.  How  much  will  a  boy  earn  in  87  hr.  at  9^  an  hour? 

4.  What  is  the  cost  of  a  flock  of  52  sheep  at  17  per  head? 

5.  At  the  rate  of  47  mi.   an  hour,  how  far  will    a    person 
travel  in  12  hr.  ? 

6.  What  is  the  cost  of  12  pr.  of  shoes  at  §4.50  per  pair,   and 
8  pr.  of  boots  at  $3.50  per  pair  ? 


MULTIPLICATION  53 

7.  What  must  be  paid  for  handling  12  loads  of  freight  at 
12.25  per  load? 

8.  In  an  orchard  there  are  13  rows  of  trees,  each  containing 
21  trees.     How  many  trees  in  the  orchard? 

9.  If  you  buy  5  pencils  at  9^  each  and  9  penholders  at  5^ 
each,  and  some  stationery  costing  25^,  how  much  change  should 
you  receive  from  a  two-dollar  bill?  from  a  ten-dollar  bill? 

10.  I  bought  6  cd.  of  wood  at  15.75  per  cord.  If  a  fifty- 
dollar  bill  is  offered  in  payment,  how  much  change  should  be 
received? 

11.  I  bought  12  bu.  of  wheat  at  $1.05.  If  I  gave  in  pay- 
ment two  ten-dollar  bills,  what  change  should  I   receive? 

12.  My  average  marketing  expenses  per  day  are  $2.10.  If  I 
offer  a  twenty-dollar  bill  in  payment  for  7  days'  expenses,  what 
change  should  I  receive? 

13.  I  sold  16  chairs  at  17  each,  and  5  tables  at  $9  each.  If 
two  one-hundred-dollar  bills  are  offered  in  payment,  how  much 
change  should  I  return?  If  a  one-hundred-dollar  bill,  a  fifty- 
dollar  bill,  and  a  twenty-dollar  bill  are  offered  in  payment,  how 
much  change  should  I  return? 

WRITTEN  EXERCISE 

In  the  following  problems  find  the  musing  numbers  by  multiply- 
ing across  and  adding  doivn.  Cheek  the  results  by  comparing  the 
sum  of  the  line  products  with  the  sum  of  the  multiplicands  multi- 
plied by  one  of  the  multipliers, 

1.  2.  3. 

15x211=?  9x1475=?  12x116.50=? 

15x346=?  9x2618=?  12x127.75=? 

15x318=?  9x1575=?  12x114.95=? 

15x721=?  9x1792=?  12  x  $29.86=? 

15x936=?  9x4936=?  12x149.88=? 

15x849=?  9x7289=?  12  x  $39.62=  ? 

15x218=X  9x8728=J^  12  x  $86.99=? 

15  X    ?    =  ?  9  X     ?     =  ?  12  X       ?      =  ? 


54  PRACTICAL   BUSINESS   ARITHMETIC 

4.  5.  6. 

12  X  192  =  ?  98  X  2178  =  ?  16  x  S18.10  =  ? 

12x721=?  98x1692=?  16  x    17.20  = 

12x836=?  98x2536=?  16  x    21.40  = 

12x456=?_  98  X  2892  =  ?  16  x    25.85=  ? 

12  X    ?    =  ?  98  X     ?     =  ?  16  X       ?      = 

Problems  such  as  the  above  are  very  helpful.  They  aiford  a  variety  of 
work  and  suggest  a  simple  method  by  which  the  student  may  test  the  cor- 
rectness of  his  results.  The  instructor  should  add  as  many  more  problems 
as  circumstances  require. 

7.  A  produce  dealer  bought  2145  bu.  of  potatoes  at  83/  a 
bushel,  and  sold  them  at  $1.05  a  bushel.     What  did  he  gain  ? 

8.  A  drover  bought  125  head  of  cattle  at  SI  5. 75  per  head. 
He  sold  65  head  at  S 23.40,  15  head  at  $13.75,  and  45  head  at 
$17.75.    Did  he  gain  or  lose,  and  how  much  ? 

9.  A  grocer  bought  14  bu.  of  apples  at  $1.35  per  bushel  and 
12  bu.  of  potatoes  at  84/  per  bushel.  He  sold  the  apples  at  40/ 
a  peck  and  the  potatoes  at  25/  a  peck.    What  did  he  gain  ? 

10.  A  bought  1247  bbl.  of  apples  at  $3.10  per  barrel.  After 
holding  them  for  three  months  he  sold  them  at  $4.80  per  barrel. 
If  he  paid  $74.82  for  storage,  and  his  loss  by  decay  was  37  bbL 
of  apples,  what  was  his  gain  ? 

11.  The  gross  weight  in  pounds,  and  tare  in  pounds,  of  25 
tubs  of  lard  are  as  follows  :  71  -  14,  70  -  15,  69  -  14,  72  -  16, 
71  - 14,  72  -  15,  70  -  15,  69  -  14,  71  -  15,  70  -  15,  69  -  14, 
71-16,  71-15,  71-14,  70-15,  68-14,  73-16,  73-15, 
70-14,  70-14,  71-15,  73-16,  74-18,  71-13,  73-16. 
Find  the  cost  at  13^  per  pound. 

12.  The  gross  weight  in  pounds,  and  the  tare  in  pounds,  of 
25  casks  of  hams  are  as  follows  :  400  -  78,  420  -  68,  420  -  71, 
403-71,  409-71,  418-68,  412-72,  407-67,  423-69, 
419-67,  426-68,  403-70,  399-69,  400-69,  425-71, 
413-72,  399-67,  412-72,  418-68,  409-71,  408-70, 
412-68,  402-71,  421-71,  403-71.  Find  the  cost  at 
18^    per   pound. 


MULTIPLICATION  55 

SHORT   METHODS    IN   MULTIPLICATION 

80.  There  are  many  short  methods  in  multiphcation,  but  of 
these  only  a  few  are  practical,  either  because  they  apply  generally 
to  problems  that  in  themselves  are  not  practical  or  because  they 
have  been  supplanted  by  the  elaborate  use  of  tables  and  mechani- 
cal devices.  A  great  many  practical  and  helpful  tables  are  in 
use  for  figuring  pay  rolls,  interest,  discount,  and  the  like.  These 
tables  are  great  time  savers.    (See  pages  229  and  321.) 

81.  The  machines  that  are  used  for  adding,  subtracting,  multi- 
plying, dividing,  and  for  setting  forth  results  in  interest  and  dis- 
count are  now  in  such  common  use  that  a  chapter  is  devoted  to 
their  consideration  in  Appendix  A  at  the  close  of  this  volume. 
These  machines  are  found  in  business  offices,  especially  where 
extensive  operations  are  to  be  performed.  Both  in  accuracy  and 
in  the  saving  of  time  they  are  most  valuable. 

82.  The  short  methods  given  herewith  have  a  wide  applica- 
tion. They  are  not  dependent  upon  formal  rules,  and  are  sug- 
gestive of  other  ways  in  which  the  student  may  exercise  his  own 
ingenuity  to  shorten  his  work  in  multiplication. 

Multiplication  by  Powers  and  Multiples  of  Ten 
oral  exercise 

1.  40  is  how  many  times  4?  60  is  how  many  times  6?  100 
is  how  man}^  times  10?     150  is  how  many  times  15? 

2.  Give  a  short  method  for  multiplying  an  integer  by  10. 

3.  400  is  how  many  times  4?  600  is  how  many  times  6? 
1000  is  how  many  times  10?     1500  is  how  many  times  15? 

4.  Give  a  short  method  for  multiplying  an  integer  by  100; 
by  1000  ;  by  10000. 

5.  How  does  the  product  of  40  x  QQ  compare  with  the 
product  of  4  X  66  X  10  ?  the  product  of  400  x  59  with  the  prod- 
uct of  4  x59  xlOO? 

6.  Give  a  short  method  for  multiplying  an  integer  by  any 
number  of  10*s,  lOO's,  or  lOOO's. 


56  PRACTICAL   BUSINESS   ARITHMETIC 

7.    Multiply  270  by  300. 

Solution.    In  the  accompanying  illustration  -^'0       =  z7  X  10 

it  will  be  seen  that  270  x  300  =  27  x  3  x  1000  300    =     3  X  100 


or  81,000.  81000  =  81x1000 

8.  Formulate  a  rule  for  finding  the  product  when  there  are 
zeros  on  the  right  of  both  factors. 

9.  $7  is  how  many  times  f  0.70?    $90  is  how  many  times 
10.90?   1500  is  how  many  times  $0.50? 

10.  State  a  short  method  for  multiplying  United  States 
money  by  10 ;  by  100 ;  by  1000. 

11.  Read  aloud  the  following,  supplying  the  missing  words : 
(a)    Annexing  a  cipher  to  an  integer  multiplies  the  integer 

by ;  annexing  two  ciphers  to  an  integer the  integer 

by . 

(J)    Removing  the  decimal  point   in  United  States  money 

one  place  to  the  right the  number  by  10 ;  removing  the 

decimal  point  two  places  to  the  right the  number  by . 

12.  Multiply  114.70  by  10 ;  by  100 ;  by  1000. 

83.    In  the  above  exercise  it  is  clear  that 

Annexing  a  cipher  to  an  integer  multiplies  the  integer  hy  10; 
and 

Removing  the  decimal  point  one  place  to  the  right  multiplies 
the  number  hy  10. 

ORAL  EXERCISE 

1.  Read  aloud  the  following  numbers  multiplied  by  10 ;  by 
100;  by  1000:     17;  285;  3712;  $413.45  ;  $1926.75 ;  4165.95. 

2.  Read  each  of  the  following  numbers  multiplied  by  20;  by 
400;  by  600;  by  5000:       16;  19 ;  37 ;  49^;  64^;  $122;  $2.60. 

3.  By  inspection  find  the  cost  of  : 

a.  750  lb.  coffee  at  30^.  g.  650  yd.  silk  at  $1.20. 

h.  500  lb.  cocoa  at  40^.  h.  140  bu.  beans  at  $3.50. 

c.  650  lb.  chocolate  at  50^.  i.  500  bu.  beans  at  $2.50. 

d.  300  bbl.  lump  salt  at  $3.  j.  240  gro.  jet  buttons  at  $3. 

e.  200  bbl.  oatmeal  at  $4.50.  k.  500  doz.  half  hose  at  $5.50. 
/.  170  bx.  wool  soap  at  $3.  I.  800  yd.  taffeta  silk  at  $1.20. 


12300 


MULTIPLICATION  57 

84.  When  the  multiplier  is  a  number  a  little  less  than  10, 
100,  or  1000,  the  multiplication  may  be  shortened  as  shown 
in  the  following  examples. 

85.  Examples,     i.    Multiply  123  by  99. 

Solution.    99  is  100  diminished  by  1;  hence,  multiply  123 
by  100  and  then  by  1  and  subtract  the  results.    The  product  is  123 

12,177.     Check  by  retracing  the  steps  in  the  process.  12177 

2.    Multiply  145  by  96. 

Solution.    96  is  100    diminished  by  4  ;  hence,  multiply  145  14ol;U 

by  100  and  then  by  4  and  subtract  the  results.    The  product  is  580 

13,920.     Check  by  retracing  the  steps  in  the  process.  13920 

WRITTEN  EXERCISE 

1.    Find  the  total  cost  of  : 

5260  bu.  rye  at  99^.  834  bu.  millet  at  95^. 

1521  bu.  rye  at  92^.  246  bu.  wheat  at  92^. 

1640  bu.  wheat  at  98^.  998  bu.  millet  at  11.04. 

2994  bu.  millet  at  97^.  998  bbl.  apples  at  11.05. 

1112  bu.  wheat  at  97^.  893  bkt.  peaches  at  11.05. 

2160  bu.  millet  at  96^.  993  bu.  clover  seed  at  13.35. 

Multiplication  by  11  and  Multiples  of  11 

86.  Example.     Multiply  237  by  11. 

Solution.  To  multiply  by  11  is  to  multiply  by  10  +  1,  Hence,  annex  a 
cipher  to  237  and  add  237  ;  or,  better  still,  add  the  digits  as  follows  :  7  ;  3  +  7  = 
10  ;  3  +  2  +  1  (carried)  =  6  ;  bring  down  2  ;  therefore,  the  result  is  2607. 

ORAL   EXERCISE 

1.  Multiply  each  of  the  following  by  11: 

14;  26;  45;  19;  16;  34;  36;  49;  64;  125;  112;  115; 
128;  192;  175;  116;  142;  $4.95;  19.62;  $4.41;  $6.82; 
15.21;  $3.65;  $4.31;  $21.12;  $14.21;  $18.32;  $3.26. 

2.  Find  the  cost  of  11  yd.  at  27^;  at  91^;  at  86^;  at 
95^;  at  $1.49;  at  $1.23;  at  $2.17;  at  $2.31;  at  $2.40;  at 
$2.50;  at  $2.75;  at  $4.35;  at  $3.15;  at  $3.10;  at  $8.13. 


58  PRACTICAL   BUSINESS   ARITHMETIC 

87.    Examples,     i.    Multiply  46  by  22. 

Solution.    22  is  U  times  2.     Multiply  46  by  11  and  by  2,  as  fol> 

lows  :  2  X  6  =  12  ;  write  2  and  carry  1.    4  +  6  =  10 ;  2  x  10  +  1  (car-  "*" 

ried)  =  21  ;  write  1  and  carry  2.    2x4  +  2  (carried)  =  10  ;  write  10.  22 

The  result  is  1012.  1012 

2.    Find  the  cost  of  122  bu.  of  potatoes  at  66^  per  bu. 

Solution.     6x2  =  12;    write  2  and  carry   1.    2+2  =  4;6x4  -too 

+  i  (carried)  =  25  ;    write   5   and   carry  2.      1  +  2=3;  6x3  +  2 
(carried)  =  20  ;  write  Oand  carry  2.    6x1+2  (carried)  =  8.    Write 


m 


The  result  is  $  80.52.  80.52 

WRITTEN   EXERCISE 

In  the  following  problems  make  all  the  extensions  mentally. 

1.  Find  the  total  cost  of  : 

11  lb.  coffee  at  42^.  115  bu.  rye  at  99^. 

14  doz.  eggs  at  21^.  215  bu.  peas  at  77^. 

64  lb.  cheese  at  22^.  344  bu.  oats  at  44)^. 

33  bu.  carrots  at  b^^,  300  bu.  grain  at  85^. 

11  bu.  potatoes  at  85^.  115  bu.  barley  at  88^. 

88  bu.  wheat  at  88/.  400  bbl.  apples  at  ^3.25. 

2.  Find  the  total  cost  of  : 

77  bu.  peaches  at  11.85.  820  bu.  rye  at  88^. 

151  bu.  corn  at  m^.  327  bu.  oats  at  33^. 

265  bu.  onions  at  80)^.  314  bu.  peas  at  m^. 

135  bu.  apples  at  82^.  110  bu.  pears  at  11.66. 

241  bu.  turnips  at  44<  880  bu.  barley  at  il.l7. 

112  bu.  tomatoes  at  55^.  100  bu.  quinces  at  11.60. 

A  careful  computer  checks  his  work  at  every  step.  The  student  who 
forms  the  habit  of  doing  this  in  all  his  computations  will  soon  find  himself 
ill  no  need  of  printed  answers  to  problems  involving  only  numerical  calcula- 
tion. 

Checks  for  multiplication  have  already  been  mentioned.  To  guard 
against  large  errors,  it  is  also  important  to  form  a  rough  estimate  of  an 
answer  before  beginning  the  solution.  Thus,  in  finding  the  cost  of  211  yd, 
of  lining  at  32^,  at  once  see  that  the  result  will  be  a  little  more  than  I63.0C 
(210  times  30^);  this  will  do  away  with  such  absurd  results  as  ^6752. 
1675.20,  or  $6.75. 


MULTIPLICATION 
3.    Copy  and  find  the  amount  of  the  following  bill: 

Boston,  Mass.,         July   21,  19 

Mrs.  GEORGE  W.  MUNSON 

168  Huntington  Ave.,  City 

Bough,  of  S.  S.  PIERCE  COMPANY 

Terms  Cash 


59 


15 

cs.  Horse-radish 

$0.66 

25 

lb.  Huyler^s  Cocoa 

.44 

31 

gal.  N.  0.  Molasses 

.63 

55 

lb.  Japan  Tea 

.48 

212 

ti  Raisins 

.11 

Multiplication  by  25,  50,  and  75 

88.  Annexing  two  ciphers  to  an  integer  multiplies  it  by  100. 
Removing  the  decimal  point  two  places  to  the  right  multiplies 
the  decimal  by  100. 

89.  Example.     Multiply  76  by  100. 

Solution.  76  x  100  =  7600.  (Annexing  the  t\w)  ciphers  gives  the  required 
result  without  the  necessity  for  a  written  solution.) 

90.  Example.     Multiply  148  by  25. 

Solution.     148  x  100  =  14,800.     14,800  -4  =  3700. 

Hence,  to  multiply  an  integer  by  25,  annex  two  ciphers  to  the  multiplicand 
and  then  divide  by  4. 

91.  Example.     Multiply  278  by  50. 

Solution.     278  x  100  =  27,800.     27,800  --  2  =  13,900. 

Hence,  to  multiply  an  integer  by  50,  annex  two  ciphers  to  the  multiplicand 
and  then  divide  by  2. 

92.  Example.     Multiply  48  by  75. 

Solution.     48  x  100  =  4800.     4800  --  4  =  1200 ;  3  x  1200  =  3600. 
Hence,  to  multiply  an  integer  by  75,  annex  two  ciphers  to  the  multiplicand, 
divide  that  product  by  4,  and  then  multiply  by  3. 


60  PRACTICAL  BUSINESS  ARITHMETIC 


State  the  product  of . 


1. 

86  X  25. 

2. 

27  X  50. 

3. 

28  X  75. 

4. 

97  X  25. 

5. 

248  X  25. 

6. 

126  X  50. 

7. 

164  X  25. 

ORAL  EXERCISE 

8.  48  X  50.  15.  64  X  75. 

9.  52  X  75.  16.  63  X  25. 

10.  67  X  50.  17.  69  X  25. 

11.  89  X  50.  18.  56  X  75. 

12.  186  X  50.  19.  240  X  75. 

13.  146  X  25.  20.  184  x  75. 

14.  204  X  50.  21.  144  X  75. 


WRITTEN   EXERCISE 

In  the  following  problems  make  all  the  extensions  mentally. 

1.  Find  the  total  cost  of : 

42  lb.  cocoa  at  40/.  27  bx.  salt  at  50/. 

45  lb.  cocoa  at  50/.  23  lb.  coffee  at  25/. 

50  lb.  coffee  at  28/.  21  lb.  candy  at  75/. 

25  lb.  raisins  at  15/.  83  lb.  chocolate  at  50/. 

28  lb.  tea  at  40/.  85  lb.  Oolong  tea  at  45/. 

2.  Find  the  total  cost  of : 

36  yd.  wash  silk  at  25/.  87  yd.  flannel  at  50/. 

25  doz.  whalebones  at?  92/.  21  yd.  cottonade  at  18/. 

97  yd.  cloth  at  75/.  25  yd.  denim  at  19/. 

25  gro.  buttons  at  35/.  17  yd.  dress  goods  at  50/. 

29  yd.  gunner's  duck  at  19/.  23  yd.  cheviot  at  21/. 

Multiplication  by  an  Even  Number  of  Hundreds 

93.  Example.     Multiply  468  by  300. 

Solution.     468  x  100  =  46,800  ;  46,800  x  3  =  140,400. 

Hence,  to  multiply  an  integer  by  an  even  number  of  hundreds,  annex  twc 
ciphers  to  the  multiplicand  and  then  multiply  by  the  significant  figure  in  the 
multiplier. 

94.  The  value  of  many  short  methods  is  that  they  enable 
one  to  write  results  quickly  without  performing  the  mechanical 
operations. 


MULTIPLICATION  61 

95.  Many  short  methods  in  niultiphcation  are  not  practical 
because  they  require  one  to  remember  so  many  things,  or  they 
apply  to  so  few  numbers  that  it  is  impossible  for  an  ordinary 
person  to  remember  them.  The  short  methods  given  in  this 
text  are  practical. 

ORAL   EXERCISE 

Find  the  product  of : 

1.  234  X  200.  7.  753  x  300.  13.  964  x  200. 

2.  175  X  600.  8.  845  x  400.  14.  554  x  300. 

3.  335  X  800.  9.  453  x  200.  15.  181  x  700. 

4.  216  X  900.  10.  256  x  400.  16.  312  x  800. 

5.  648  X  100.  11.  145  X  800.  17.  237  x  600. 

6.  452  X  500.  12.  333  x  700.  18.  122  x  900. 

Multiplication  by  Numbers  from  101  to  109  Inclusive 

96.  Examples,     l.   Find  the  cost  of  64  bu.  of  wheat  at  $1.02. 

Solution.     2  x  64  =  128  ;  write  28  and  carry  L     1  x  64  +1  =  "^ 

65 ;  write  65.      The  result  is  $  65.28.  1.02 

Some  persons  may  prefer  to  work  this  problem  as  follows  ;  64  65.28 
bu.  at$l  =$64;  64  bu.  at  2^  =  $1.28;  $64  +  $1.28  =  $65.28. 

2.   Find  the  cost  of  251  bu.  of  barley  at  11.04. 

Solution.    4  x  51  =  204  ;   write  04  in  the  product  and  carry  2.  251 

4x2  +  2  (carried)  -f  1  (the  right-hand  figure  of  the  nuiltiplicand)  -i  (\a 

=  11  ;  write  1  and  carry  1.     1  x  25  +  1  (carried)  =  26  ;  write  26.  ' 

The  result  is  $  261.04.  261. 04 

97.  Similarly  multiply  by  such  numbers  as  201,  302,  and  405. 

98.  Example.     Find  the  cost  of  124  bu.  of  beans  at  $  2.05. 

Solution.    5  x  24  =  120.     Write  20   and   carry   1.      5x1+1  124 

(carried)  +2x4  (the  right-hand  figure  of  the  multiplicand)  =  14  ;  90^ 

write  4  and  carry  1.     2  x  12  +  1  (carried)  =  25  ;  write  25.     The  ' 

result  is  $  254.20.  254. 20 

Some  persons  may  prefer  the  following  solution  :  124  bu.  at  $2  =  $248; 
124  bu.  at  5)?  =  $6.20;  $248  +  $6.20  =  $254.20.  The  student  should  try 
to  exercise  his  own  ingenuity  in  all  this  work. 


62 


PRACTICAL   BUSINESS   ARITHMETIC 


WRITTEN   EXERCISE 


Find  the  value  of: 

1.  215  T.  coal  at  16.05. 

2.  224  bu.  rye  at  $1.02. 

3.  215  bu.  wheat  at  $1.02. 

4.  318  bu.  barley  at  1 1.05. 

5.  124  bbl.  apples  at  12.05. 

6.  116  bbl.  onions  at  $  1.08. 

7.  232  bbl.  potatoes  at  |2.05. 


8.  802  bu.  peas  at  74  ^. 

9.  104  bu.  corn  at  89  ^. 

10.  103  bu.  beets  at  85  ^. 

11.  205  bu.  turnips  at  54  ^. 

12.  215  bu.  pears  at  11.05. 

13.  411  bu.  plums  at  11.08. 

14.  206  bu.  parsnips  at  98^. 


Miscellaneous  Short  Methods 

99 .  When  one  part  of  the  multiplier  is  contained  in  another 
part  a  whole  number  of  times,  the  multiplication  may  be  short- 
ened as  shown  in  the  following  examples. 

100.    Example.     Multiply  412  by  357. 


Solution.  35  is  5  times  7.  7  x  412  =  2884,  which 
write  as  the  first  partial  product.  5  x  2884  =  14,420, 
which  write  as  the  second  partial  product. 

Check.  Interchange  the  multiplier  and  multipli- 
cand and  remultiply.  4  x  357  =  1428  ;  3  x  1428  =4284. 
Add.  Since  the  results  by  both  multiplications  agree, 
the  work  is  probably  correct. 


412 

357 


357 
412 


2884 
14420 


1428 
4284 


1470.84       147084 


101.    Example.     Multiply  214  by  756. 

Solution.     56  is  8  times  7.     7  x  214  =  1498,  which  we  write  as 
the  first  partial  product.     8  x  1498  =  11,984,  which  we  write  as  the      TTog 
second  partial  product.    The  sum  (161,784)  of  these  partial  products         .j  .j  ^^  . 


214 

756 


is  the  entire  product. 

Check  as  in  problem  1.     (See  also  pages  89  and  90.) 


161784 


WRITTEN   EXERCISE 

Find  the  product  of: 

1.  319  X  248.  3.    728  x  287. 

2.  927  X  279.  4.    848  x  369. 

102.    The  above  short  methods  are  practical  in  a  limited  num- 
ber of  problems. 


MULTIPLICATION 


63 


WRITTEN  REVIEW  EXERCISE 


1.    Use  6  as  a  multiplier  for  each  column.      Check.      (See 
page  53.) 


a. 

h. 

c. 

d. 

e. 

56 

U 

39 

126 

215 

48 

63 

58 

232 

175 

73 

52 

82 

311 

243 

49 

65 

72 

135 

223 

45 

55 

85 

144 

183 

^^ 

47 

19 

225 

253 

11 

88 

92 

245 

127 

2.  Use  8  as  a  multiplier  for  each  column.     Check. 

3.  I  bought  15  A.  of  land  at  $275  per  acre  and  laid  it  out  in 
100  city  lots.  After  expending  S6750  for  grading  and  taxes, 
S257  for  ornamental  trees,  and  S250  for  advertising,  I  sold 
15  lots  at  $625  each,  35  lots  at  $415  each,  and  exchanged  the 
remainder  for  a  farm  of  120  A.,  which  I  immediately  sold  at 
S195  per  acre.     Did  I  gain  or  lose,  and  how  much? 

4.  Copy  and  find  the  amount  of  the  following  bill: 


Rochester,  N.Y.,        July  26, 

Mr.    F.    C.    GORHAM 

120  Spring  Street,  City 

Bouglit  of  C.  E.  Ferguson  G?  Son 

Terms    50    da. 


19 


37  bu. 

Oats 

$0.40 

50   u 

Corn 

.67 

76   n 

Wheat 

1.02 

75   u 

Rye 

1,04 

95   u 

Beans 

4.00 

16   u 

Clover 

Seed 

3.50 

26   M 

Millet 

.99 

64 


PRACTICAL   BUSINESS    ARITHMETIC 


WRITTEN    REVIEW 

Copy  these  examples ;  add  the  checks  in  the  Checks  in  Detail  cohimn 
and  enter  the  totals  in  the  Total  Checks  column ;  find  the  new  balance,  the 
total  old  balance,  the  total  checks,  the  total  deposits,  and  check  the  work. 


Checks  in 

Total 

Name 

Balance 

Detail 

S180.55 

Checks 

Deposits 

Bala] 

A 

S313.25 

211.15 
165.43 
208.19 

? 

S  278.40 

? 

B 

285.67 

100.55 
145.97 

? 

327.44 

9 

C 

186.53 

200.12 

45.67 

118.95 

? 

198.45 

? 

D 

276.65 

205.18 

? 

210.50 

9 

E 

612.40 
64.25 

9 

918.75 

9 

xU 

F 

347.85 

103.86 
6.84 
? 

9 

? 

? 

? 

? 

? 

2. 

' 

Checks  in 

Total 

Name 

Balance 

Detail 

Checks 

Deposits 

Bala 

A 

$195.63 

S  214.70 

71.20 

8.50 

? 

S174.25 

? 

B 

98.40 

102.45 

74.65 

123.52 

? 

115.68 

9 

C 

153.30 

10.55 
75.20 
55.34 

? 

89.48 

? 

D 

386.54 

7.35 

? 

275.40 

? 

172.38 

MULTIPLICATION  65 

A   WRITTEN   REVIEW   TEST 

Write  the  following  i^rohlerm  from  dictation,  and  complete  the. 
work.    Time,  approximately,  forty  minutes,  including  the  dictation. 
Mental  extensions  only. 

1.  Write  in  one  column,  and  find  the  total  value : 

78  yd.  at  11/  55  yd.  at  55/ 

69  yd.  at  25/  91  yd.  at  50/ 

60  yd.  at  85/  89  yd.  at  99/ 

45  yd.  at  98/  75  yd.  at  90/ 

37  yd.  at  97/  76  yd.  at  70/ 

112  yd.  at  99/  125  yd.  at  98/ 

2.  Write  in  one  column,  and  find  the  total  value : 

76  yd.  at  Sl.lO  82  yd.  at  S1.05 

55  yd.  at  S1.06  65  yd.  at  S1.20 

108  yd.  at  $1.11  130  yd.  at  $1.09 

m  yd.  at  $1.25  83  yd.  at  $1.50 

88  yd.  at  $1.04  97  yd.  at  $1.03 

67  yd.  at  $1.02  137  yd.  at  $1.01 

3.  Write  hi  one  column  ;  use  11  as  the  multiplier,  and  check 
the  results: 

49,    16,    34,    78,    57,    73,    85,    94,    59,    64,    56,    81. 

4.  Write  in  one  column ;  use  6  as  the  multiplier,  and  check 
the  results : 

125,  212,  350,  175,  162,  224,  319,  452,  133,  145,  121,  142. 

5.  Write  in  one  column ;  use  8  as  the  multiplier,  and  check 
.the  results : 

45,    75,    62,    29,    76,    61,    19,    34,    85,    92,    27,    77. 

6.  Write  in  one  column ;  square  each  number,  and  total  the 
products : 

25,    55,    15,    45,    75,    35,    85,    65,    95. 

7.  The  text,  page   63,  problem  3,  in   the  Written  Review 

Exercise. 


CHAPTER  VII 

DIVISION 
ORAL  EXERCISE 

1.  What  is  the  product  of  12  times  15?  How  many  times 
is  15  contained  in  180  ?     What  [s.j\  of  180  ? 

2.  How  much  is  11  times  il7?  How  many  times  is  il7 
contained  in  $187  ?     What  is  J^  of  $187  ? 

3.  What  is  the  product  of  9  times  12  ft.?  How  many  times 
is  12  ft.  contained  in  216  ft.?     What  is  J^  of  225  ft.? 

4.  When  one  factor  and  the  product  are  given,  how  is  the 
other  factor  found  ? 

103.  The  process  of  finding  either  factor  when  the  product 
and  the  other  factor  are  given  is  called  division. 

104.  The  known  product  is  called  the  dividend;  the  known 
factor,  the  divisor;  the  unknown  factor,  when  found,  the 
quotient. 

105.  The  part  of  the  dividend  remaining  when  the  division 
is  not  exact  is  called  the  remainder. 

While  definitions  such  as  the  above  should  not  be  memorized,  the  ideas 
which  they  express  should  be  thoroughly  understood. 

106.  Since  6  times  7  ft.  =  42  ft.,  42  ft.  -f-  7  ft.  =  6,  and 
42  ft.  -^  6  =  7  ft.     It  is  therefore  clear  that 

1.  If  the  dividend  and  divisor  are  concrete  numbers^  the  quo- 
tient is  an  abstract  number  ;  and 

2.  If  the  dividend  is  concrete  and  the  divisor  abstract,  the  quo- 
tient is  a  concrete  number  like  the  dividend. 

In  §106  it  will  be  seen  that  there  are  two  kinds  of  division :  42  ft.  h-  7  f t.  = 
6  is  sometimes  called  measuring,  because  42  ft.  is  measured  by  7  ft. ;  42  ft.  -^ 
6  =  7  ft.  is  sometimes  called  partition,  because  42  ft.  is  divided  into  6  equal 
parts. 

66 


DIVISION  67 


ORAL  EXERCISE 


1.  Divide  by  2 :  18,  32,  78,  450,  642,  964,  893. 

2.  Divide  by  3 :  27,  57,  72,  423,  642,  963,  845. 

3.  Divide  by  4 :  64,  88,  92,  488,  192,  396,  728. 

4.  Divide  by  5:  Qb,  85,  95,  135,  275,  495,  725. 

5.  Divide  by  6 :  84,  96,  54,  246,  546,  672,  846,  636. 

6.  Divide  by  7 :  63,  84,  91,  217,  497,  714,  791,  921. 

7.  Divide  by  8 :  72,  56,  88,  248,  640,  128,  144,  152. 

8.  Divide  by  4 :  56,  96,  77,  241,  168,  128,  920,  848. 

9.  Divide  by  6 :  78,  96,  56,  272,  848,  190,  725,  966. 
10.  Divide  by  9 :  98,  72,  49,  279,  819,  720,  189,  918. 

ORAL   EXERCISE 

1.  16  ft.  -^  2  =  ?  24  ft.  -^  8  ft.  =  ? 

2.  125  ^  5  =  ?     129.75  -  5  =  ?   1129.78  ^  9  =  ?  13.40  h- 
4  =  ? 

3.  126  yd. --3  yd.  =  ?     1125-25  =  ?     $6.25 -■  81.25  =  ? 

4.  If  9  T.  of  coal  cost  149.50,  what  is  the  cost  per  ton? 

Solution,    f; 49.50  -t-  9  =  $  5 ;  subtracting  9  times  $ 5,  the  re-  $ 5.50 

suit  is  $4.50  undivided  J    $4.50 -^  9  =  $0.50.      Therefore  the  0^*149  5Q 

quotient  is  $5.50. 

5.  At  $1.75  a  yard,  how  many  yards  can  be  bonght  for  135? 

Solution.     The   divisor  contains  cents    and    it  is  therefore  20 

better  to  first  change  both  dividend  and  divisor  to  cents.    It  is      -irj cNqcnn 
found  that  $35  would  buy  20  times  as  many  yards  as  $1.75  ,  or  ^ 

20  yd. 

6.  If  5  T.  of  coal  cost  131.25,  what  is  the  cost  per  ton? 

7.  At  1 2.50  per  yard  how  many  yards  can  be  bought  for  $  550  ? 

ORAL   EXERCISE 

1.  How  many  weeks  in  98  da.  ? 

2.  What  is  2^  of  2250  bbl.  of  apples?  ^i^?  J?  ^\? 

3.  The  quotient  is  8  and  the  dividend  128.      What  is  the 
divisor? 

4.  How  many  times  can  18  be  subtracted  from  75,  and  what 
will  remain? 


68  PRACTICAL   BUSINESS    ARITHMETIC 

5.  At  15^  per  pound,  Iiow  many  pounds   of  beef  can  be 
bought  for  $6.30? 

6.  The  quotient  is  5,  the  divisor  23,  and  the  remainder  2. 
What  is  the  dividend  ? 

7.  If  5  men  earn  117.50  a  day,  how  much  can  8  men  earn 
in  2  da.  at  the  same  rate? 

8.  What  is  the  nearest  number  to  150  that  can  be  divided 
by  9  without  a  remainder? 

9.  If  there  are  960  sheets  in  40  qr.   of  paper,  how  many 
sheets  in  5  qr.  ?  in  11  qr.  ? 

10.  If  6  bbL  of  apples  are  worth  $  21,  what  are  24  bbL  worth 
at  the  same  rate  ?  36  bbL  ? 

11.  If  17  bbL  of  flour  cost  S85,  what  will  25  bbL  cost  at  the 
same  rate  ?  32  bbl.  ?  48  bbl.  ?   34  bbl.  ? 

12.  If  8  be  added  to  a  certain  number,  7  can  be  subtracted 
from  that  number  7  times.    What  is  the  number  ? 

13.  If  20  yd.  of  cloth  cost  $60,  for  how  much  per  yard 
must  it  be  sold  to  gain  1 25?   to  gain  $15? 

14.  A  grocer  sold  250  oranges  at  5^  each  and  gained  $5. 
How  much  did  he  pay  a  dozen  for  the  oranges? 

15.  A  grocer  pays  $3  for  20  doz.  of  eggs.  At  what  price  per 
dozen  must  he  sell  them  in  order  to  gain  $1.50? 

16.  At  $2.50  per  yard,  how  many  yards  of  cloth  can  be 
bought  for  $75?  for  $150?  for  $2500?  for  $750? 

17.  How  many  days'  labor  at  $3.50  per  day  will  pay  for  2  T. 
of  coal  at  $7  a  ton  and  5  lb.  of  tea  at  70 J^ per  pound? 

18.  A  clothier  pays  $96  for  a  dozen  overcoats.  At  how 
much  apiece  must  he  retail  them  to  gain  $48  on  the  lot? 

19.  A  man  exchanged  1140  bu.  of  wheat  at  $1  per  bushel 
for  flour  at  $6  per  barrel.      How  many  barrels  did  he  receive? 

20.  It  was  found  that  after  15  had  been  subtracted  5  times 
from  a  certain  number  the  remainder  was  4.  What  was  the 
number? 

21.  A  man  contracts  a  debt  of  $175  which  he  promises  to 
pay  in  weekly  installments  of  $3.50  each.  After  paying  $35, 
how  many  more  payments  has  he  to  make? 


DIVISION  69 

107.    Examples,     i.  Divide  4285  by  126. 

Complete  Operation  Required  Work 


126)4285  126)4285 

378            =3  times  126  378 

505  undivided  505 

504          =4  times  126  504 

1  undivided  1 


Check.     34  x  126  +  1  =  4285 

The  remainder  cannot  always  be  written  as  a  part  of  the  quotient.  Thus 
in  the  problem,  "At  $7  per  head  how  many  sheep  can  be  bought  for  $37," 
we  cannot  say,  "  5f  sheep,"  but  "  5  sheep  and  $2  remaining." 

2.  A  farmer  received  $283.25  in  payment  for  275  bu.  of  wheat; 
How  much  was  received  per  bushel  for  the  wheat? 

11.03 

Solution,  f  283.75  -  275  =  $  1  and  $8.25  undivided.  275)$283.25 
$8.25  -f-275  =$0.03.     $1.03  per  bushel  was  therefore  re-  9fTr 

ceived  for  the  wheat.  — 

Check.     275  times  $  1.03  =  $283.25.  °  25 

825 

108.  Work  in  division  may  be  abridged  by  omitting  the 
partial  products  and  writing  only  the  partial  dividends. 

109.  Example.     Divide  $614.80  by  232. 

Solution.  Omit  writing  the  products;  subtract  mentally  and  write  the 
remainder  only  :   2  x  232  =  464  ;  464  subtracted  from  614 

equals  150  ;  omit  the  writing  of  the  464.    Proceed  as  follows  :  •IS)  Z.bO 

2  times  2  plus  0  =  4  ;  2  times  3  plus  5  =  11.    2  times 2  + 1  =  5,  232)S614.80 

and  5  plus  1  =  6.     Bring  down  8.     6  times  2  plus  6  =  18  ;  150  8 

6  times  3  plus  1  =  19,  and  19  +1=  20  ;  6  times  2  plus  2  =14,  H  (30 

and  14  plus  1  =  15.    Bring  down  0  and  proceed  as  before.  Q  QQ 

WRITTEN   EXERCISE 

1.  Find  the  cost  of  8800  lb.  of  oats  at  45/  per  bushel  of  32  lb. 

2.  How  many  automobiles,  at  S650  each,  can  be  purchased 
for  84,225,000? 

3.  By  what  number  must  8656  be  multiplied  to  make  the 
product  8,223,200? 


70 


PEACTICAL   BUSINESS   ARITHMETIC 


4.  If  120  bbl.  of  flour  cost  |660,  what  will  829  bbl.  cost  at 
the  same  rate  ? 

5.  The  product  of  two  numbers  is  1,928,205.  If  one  of  them 
is  621,  what  is  the  other  ? 

6.  If  380  T.  of  coal  can  be  bought  for  $3040,  how  many 
tons  can  be  bought  for  f  3600  ? 

7.  How  many  cords  of  128  cu.  ft.  in  a  pile  of  wood  con- 
taining 235,820  cu.  ft.  ?     What  is  it  worth  at  14.50  per  cord  ? 

8.  A  speculator  sold  a  quantity  of  apples  that  cost  $2500 
for  $4750.  If  his  gain  per  barrel  was  $1.12^^,  how  many 
barrels  did  he  buy  ? 

9.  A  man  received  a  legacy  of  $11,375  which  he  invested 
in  railroad  stock.  He  paid  a  broker  $  125  to  buy  stock  at 
$112.50  per  share.     How  many  shares  were  bought? 

10.  A  dealer  bought  250  T.  of  coal  by  the  long  ton  of  2240  lb. 
at  S6.50  per  ton.  He  retailed  the  same  at  S  8.25  per  short  ton  of 
2000  lb.    What  was  the  total  gain  ? 

11.  In  a  recent  year  there  were  produced  in  the  United  States 
730,627,000  bu.  of  wheat  on  '45,814,000  A.  What  was  the  yield 
per  A.  ?    What  was  the  total  yield  worth  at  90/  per  bu.  ? 

12.  Copy  and  complete  the  following  table  of  corn  statistics. 
Check  the  work.  (The  total  yield  multiplied  by  the  price  per 
bushel  should  equal  the  total  valuation.) 

Principal  Corn-growing  States  in  a  Recent  Year 


State 

Yield  in  Bitshels 

Farm  Price 
per  Bushel 

Farm  Valuation 

Illinois 

Iowa 

Nebraska 

Missouri 

Indiana 

Kansas 

426  320  000 

? 

? 
199  364  000 
174  225  000 

62j^ 
62j* 

Q2^ 
62f 

264  318  400 
267  853  020 
113  221  920 
151  220  480 

? 

? 

Total 

? 

62/ 

9 

13-15.  Make  and  solve  three  self -checking  problems  in  division 


DIVISION  71 

SHORT  METHODS   IN  DIVISION 

Powers  and  Multiples  of  10 

oral  exercise 

1.  How  many  times  is  10  contained  in  50?  100  in  800? 
1000  in  9000? 

2.  Cutting  off  a  cipher  in  30  divides  it  by  what  number? 

3.  Cutting  off  two  ciphers  in  800  divides  it  by  what  number  ? 

4.  Cutting  off  three  ciphers  in  11,000  divides  it  by  what 
number  ? 

5.  Read  aloud,  supplying  the  missing  words  : 

a.  The  number  of  lO's  in  any  number  may  be  found  by 
cutting  off  the  units'  figure ;  the  number  of  lOO's  by  cutting 

off  the and figures ;  the  number  of  by  cutting 

off  the  hundreds'  and  tens'  and  units'  figures. 

h.    In  4561  there  are  456  tens  and  1  unit,  or  456  Jq  tens ;  45 

and  61  units,  or  45^yQ  hundreds ;  and thousands  and 

561  units,  or  ^^i'i^  tliousands. 

6.  How  many  times  is  $0.10  contained  in  f  1  ?  -$0.01  in 
II?  10.001  in  II? 

7.  Whatis-Jo  of  II?     ^l^ofll?     loVoof^l^ 

8.  Read  aloud,  supplying  the  missing  words:  10.60  is 

of  %^  ;  10.06  is of  16  ;     10.006  is of  %^, 

9.  Formulate  a  short  method  for  dividing  United  States 
money  by  10  ;  by  100  ;  by  1000. 

10.  By  inspection  find  the  quotient  of  : 

a.   736 -f- 10.  e.  1271-^100.         L  2140  lb.  ^  100. 

h.    1531-^100.  /.  1519.50-10.     j.  3145  1b.  ^100. 

c.  16351-1000.         ^.  184.50 -^  100.      A^.  3416  ft.  -  1000. 

d.  311219-10000.     h.  12150-^1000.     I.  1279  posts -f- 100. 

11.  Read  aloud,  supplying  the  missing  amounts : 
a.    6400-1600  = ;  640^10  = . 

h.    27000  ^  9000  = ;    2700  -^  900  = ;    270  -  90  = 

;   27-^9= . 

c.    18801  -  90  = 9 ;  214200  ^  700  =  2142  -f- . 


72  PRACTICAL   BUSINESS   AEITHMETIC 

12.  How  is  the  quotient  affected  by  like  changes  in  both 
the  dividend  and  divisor  ? 

13.  Divide  1323  by  400. 

Solution.     Cut  off  the  two  ciphers  in  the  divisor  and  two  ^11  f 

digits  in  the  right  of  the  dividend,  thus  dividing  both  dividend  4100^13123 
and  divisor  by  100.     4  is  contained  in  13  three   times  with  a     '  ^ 

remainder  1  hundred.     Adding  to  this  remainder  the  23  units  _ 

remaining  in  the  dividend  after  dividing  by  100,  the  true  re-  123 

mainder  is  123, which  write  in  fractional  form. 

14.  Read  aloud,  supplying  the  missing  amounts  :  1611  -4-  400 

= ;    2847 -=-700  = ;    1531^300  = ;    16139^ 

4000  = . 

15.  Formulate  a  rule  for  dividing  a  number  by  any  multiple 
of  ten. 

16.  State  the  quotient  of  : 

a,  1231-^30.  /.  96131-400.  h,  63571^3000. 

5.  9647 -^  40.  g.  84199 -- 700.  I.  16657-4000. 

c.  6551  H- 50.  h.  64137 -V- 800.  m,  36119-6000. 

d.  4273^70.  .  i.  45117 -- 900.  n.  18177^-9000. 

e.  8197 -f- 90.  /.  25121-500.  o.  42113^7000. 


ORAL  REVIEW  EXERCISE 

The  diagram  on  the  opposite  page  is  a  portion  of  the  New  York  Central 
time-table  giving  the  distances  between  many  of  the  stations  from  New 
York  City  to  Suspension  Bridge,  and  the  time  taken  by  two  different  trains 
to  travel  this  route. 

1.  How  many  miles  between  New  York  City  and  Pough- 
keepsie?  between  Poughkeepsie  and  Utica?  between  Utica  and 
Syracuse?  between  Syracuse  and  Rochester?  between  Rochester 
and  Buffalo?  between  Buffalo  and  Niagara  Falls? 

2.  What  is  the  distance  between  New  York  City  and  Syra- 
cuse? between  Poughkeepsie  and  Niagara  Falls?  between 
Rochester   and    Suspension    Bridge? 

3.  How  many  miles  between  Ludlow  and  each  station  below 
it?  between  Poughkeepsie  and  each  station  below  it?  between 
Tarry  town  and  each  station  below  it? 


DIVISION 


73 


4.  How  many  miles  between 
below  it?   between   Oscawana  and 
each  station  below  it? 

5.  At  2j^  per  mile,  what  is  the 
fare  from  New  York  to  Niagara 
Falls  ?  from  Poughkeepsie  to  Syra- 
cuse ?  from  Buffalo  to  Utica  ?  from 
Troy  to  Yonkers? 

6.  At  2;^  per  mile,  what  is  the 
fare  from  Rochester  to  Syracuse? 
from  Rensselaer  to  Suspension 
Bridge?  from  Albany  to  Niagara 
Falls?  from  Syracuse  to  Buffalo? 
to  Albany  ? 

7.  How  long  does  it  take  train 
No.  93  to  travel  the  first  30  mi. 
toward  Poughkeepsie?  the  first  74 
mi.   toward  Albany? 

8.  How  long  is  train  No.  93 
in  making  the  run  from  Fishkill 
Landing  to  Camelot?  This  is  ap- 
proximately how  many  miles  an 
hour? 

9.  How  long  does  it  take  train 
No.  73  to  make  the  run  from  Utica 
to  Syracuse  ?  How  long  does  it  take 
train  No.  73  to  make  the  run  from 
Fishkill  Landing  to  Chelsea  ?  This 
is  approximately  how  many  miles 
an  hour? 

10.  Add  each  number  in  the  col- 
umn marked  "  Miles "  to  the  one 
immediately  below  it. 


Montrose  and  each  station 


63 


NORTH 

AND 

WEST  BOUND 


Lv 


New  York 
Grand  Cent.  Sta. . 

125th  St.  Sta 

138th  St.  Sta 

High  Bridge 

Morris  Heights 

Kings  Bridge 

Spuyten  Duyvil 

Riverdale 

Mt.  St.  Vincent 

Ludlow 

Yonkers 

Glenwood 

Hastings-on-Hudson 

Dobbs'  Ferry 

Ardsley-  on  -Hudson 

Irvington 

Tarrytown 

Scarborough 

Ossining = 

Croton-on-Hudson .. 

Oscawana 

Crugers 

Montrose 

Peekslcill 

Highlands 

Garrison 

Cold  Spring 

Storm  King 

Dutchess  June 

Fishkill  Landing 

Chelsea 

New  Hamburg 

Camelot 

Poughkeepsie Ar 

Poughkeepsie Lv 

Hyde  Park " 

Staatsburgh »' 

Rhineclitf  (Rh'b'k)..  " 

Barrytown " 

Tivoli •' 

Germantown '• 

Linlithgo " 

Greendale *♦ 

Hudson '* 

Stockport " 

Newton  Hook " 

Stuyvesant " 

Schodack  Landing..  " 

Castleton " 

Rensselaer " 

Albany Ar. 

Troy " 


Utica 

Syracuse- 
Rochester. 
Buffalo 


Ar. 


Niagara  Falls Ar. 

Suspension  Bridge " 


73 


121110  6t01 
12*23  6^13 
6.15 
6.21 
625 
6.29 
6.33 


12.46 


1.25 


1.47 


2  24 
2.31 


2.53 
3.05 


5.50 
6^50 


8540 
9.55 


2513 
2£20 


6.43 
6.46 
6.52 
6.59 
7.01 
7.05 
7.12 
7.19 
7.25 
7.31 
7.34 
7.37 
7.41 
7.49 
7.59 
8.06 
8.12 
8.16 
8.21 
8.27 
8.34 
8.40 
8.46 
8*55 


Thus,  9, 12, 16, 24,  34, 45,  58,  etc.  In  add- 
ing 89  and  95  think  of  179  and  5,  or  184  ;  in 
adding  143  and  149  think  first  of  243  and  49  and  then  of  283  and  9,  or  292. 


74  PEACTICAL   BUSINESS   AEITHMETIC 

11.  Multiply  each  number  in  the  column  marked  "  Miles " 
by  5;  by  8;  by  3 ;  by  7 ;  by  6 ;  by  4;  by  9. 

The  numbers  in  the  portion  of  the  time-table  illustrated  may  be  used 
for  such  other  exercises  as  may  seem  necessary  at  this  point.  Students 
should  be  impressed  with  the  importance  of  being  able  to  add,  subtract, 
multiply,  and  divide  numbers  in  any  relative  position.         « 

12.  Five  parts  of  120  are  15,  18,  32,  10,  and  20.  Find  the 
sixth  part,  and  multiply  it  by  15. 

13.  From  a  flock  of  170  sheep  I  sold  at  different  times  12, 
18,  32,  and  9.     How  many  sheep  remained  ? 

14.  Multiply  by  11  each  of  the  following  numbers:  21,  32, 
43,  54,  65,  76,  87,  98,  61,  28,  37,  14,  21,  62. 

15.  At  22  /  per  yard,  what  will  18  yd.  cost  ?  21  yd.  ?  36  yd.  ? 
56  yd.  ?  29  yd.  ?   73  yd.  ?  94  yd.  ?   72  yd.  ? 

16.  Multiply  each  number  in  problem  15  by  33 ;  by  44. 

WRITTEN   REVIEW   EXERCISE 

1.  Find  the  total  cost  of  the  articles  in  problem  3  of  the 
oral  exercise,  page  56.  Find  the  total  of  the  products  in  the 
oral  exercise,  page  60. 

2.  A  mechanic  earns  S125  per  month  and  his  monthly  ex- 
penses average  S72.  If  he  saves  the  remainder,  how  long  will 
it  take  him  to  save  $4352  ? 

3.  I  spent  $24,800  for  apples  at  $2.50  per  barrel  The  loss 
from  decay  was  equal  to  74  bbl.  What  was  my  gain,  if  the 
remainder  of  the  apples  sold  for  $3.75  per  barrel,  and  my 
expenses  for  storage  were  $675.80? 

4.  During  a  certain  week  a  contractor  employed  help  as 
follows:  34  hands,  8  hr.  per  day,  for  5  da.,  at  15/  per  hour; 
16  hands,  9  hr.  per  day,  for  6  da.,  at  25/  per  hour;  29  hands, 
10  hr.  per  day,  for  6  da.,  at  18/  per  hour.     Find  the  amount  due. 

5.  In  a  recent  year  there  were  produced  on  37,917,000  A. 
in  the  United  States  1,418,337,000  bu.  oats,  valued  on  the  farm 
at  31.3/  per  bushel.  What  was  the  average  yield  per  acre? 
What  was  the  value  of  the  year's  crop  ? 


DIVISION 


75 


6.  Without  copying  find  (a)  the  total  number  of  raihvay 
employees  in  the  United  States  in  1910  and  (b)  the  total  num- 
ber per  one  hundred  miles  of  line  in  the  same  year. 

Railway  Employees  in  the  United  States 


1910 

1911 

Total 

Number 

Average 

Total 

Number 

Average 

Class 

Number 

PER 

100  Mi. 

Daily 
Wages 

Number 

PER 

100  Mi. 

Daily 
Wages 

General  officers 

5.476 

2 

$13.27 

5,628 

2 

$12.99 

Other  officers 

9,392 

4 

6.22 

10,196 

4 

6.27 

General  office  clerks 

76,329 

32 

2.40 

76,513 

31 

2.49 

Station  agents 

37,379 

16 

2.12 

38,277 

16 

2.17 

Other  station  men 

153,104 

64 

1.84 

153,117 

62 

1.89 

Engineers 

64,691 

27 

4.55 

63,390 

26 

4.79 

Firemen 

68,321 

28 

2.74 

66,376 

27 

2.94 

Conductors 

48,682 

20 

3.91 

48,200 

20 

4.16 

Other  trainmen 

136,938 

57 

2.69 

133,221 

54 

2.88 

Machinists 

55,193 

23 

3.08 

55,207 

22 

3.14 

Carpenters 

68,085 

28 

2.51 

65,989 

27 

2.54 

Other  shopmen 

225,196 

94 

2.18 

226,785 

92 

2.24 

Section  foremen 

44,207 

18 

1.99 

44,466 

,  18 

2.0f 

Other  trackmen 

378,955 

157 

1.47 

363,028 

147 

1.50 

All  other  employees 

229,806 

95 

2.01 

227,779 

93 

2.08 

7.  Without  copying  find  (a)  the  total  number  of  railway 
employees  in  the  United  States  in  1911  and  (5)  the  total  num- 
ber per  one  hundred  miles  of  line  in  the  same  year. 

8.  Find  the  total  salaries  paid  to  railway  employees  in  1910  ; 
in  1911. 

9.  Find  the  average  daily  wages  paid  to  railway  employees 
in  1910;  in  1911. 

10.    In  a  recent  year  four  leading  railway  systems  had  out- 
standing bonds  as  follows : 

a,  $761,963,000.  c.  $1,096,773,410. 

h.  $576,300,000.  d.  $428,649,000. 

Find  the  average  amount  of  the  bonds  outstanding. 


76  PRACTICAL   BUSINESS   ARITHMETIC 


WRITTEN  REVIEW 


In  these  problems  divide  across,  and  then  add  the  dividend  column 
and  the  quotient  column,  Chech :  divide  the  total  of  the  dividend 
column  by  the  divisor,  and  this  quotient  should  equal  the  sum  of  the 
individual  quotients.      Time,  approximately,  fifteen  minutes. 


1. 

2. 

3. 

36  -^  4  =  ? 

-1 

45-f-5  =  ?     ' 

m-^Q^"^ 

48  -^  4  =  ? 

75^5  =  ?  . 

72  -J-  6  =  ? 

56  ^  4  =  ? 

1  ^ 

95  ^  5  =  ?      H 

84  ^  6  =  ? 

24  ^  4  =  ? 

b 

65^5  =  ?/, 

78  -^  6  =  ? 

84  -V-  4  =  ? 

^'/ 

35^5  =  ? 

48-^6  =  ?  ' 

44^4  =  ? 

b 

55  -f-  5  =  ? 

36  -^  6  =  ? 

64  ^  4  =  ? 

•  15^5  =  ? 

54  -  6  =  ? 

76  ^  4  =  ? 

'  J 

40  ^  5  =  ? 

42  -f-  6  =  ? 

4. 

^?- 

?  -i-5  =  ? 

?  -6  =  ?  ^ 

5. 

6. 

98-^7-? 

88^2  =  ? 

48^3  =  ? 

84  ^  7  =  ? 

;  /i.- 

'76^2  =  ? 

54  -^  3  =  ? 

63^7  =  ? 

"■'■ 

58  ^  2  =  ? 

69-^3  =  ? 

49  H-  7  =  ? 

64  -^  2  =  ? 

72^3  =  ? 

91-^7  =  ? 

82-f-  2  =  ? 

84  ^  3  =  ? 

56  -f-  7  =  ? 

94  H-  2  -  ? 

93  -f-  3  =  ? 

77^7-? 

52  -  2  =  ? 

87-f-3  =  ? 

42^7  =  ? 

74  ^  2  =  ? 

54  -f-  3  =  ? 

?  -^  7  =  ? 

?  -f-2  =  ? 

?  -V-  3  =  ? 

7. 

8. 

9. 

126-^2  =  ? 

144  ^  4  =  ? 

129  ^  3  =  ? 

152 -f- 2=:? 

124-h4  =  ? 

114  ^  3  =  ? 

134  -f-  2  =  ? 

152-4  =  ? 

108  ^  3  =  ? 

168^2  =  ? 

148  -^  4  =  ? 

147_j.3  =  ? 

184  -f-  2  =  ? 

176^4  =  ? 

189^3  =  ? 

156  -^  2  =  ? 

184  -  4  =  ? 

165-^3  =  ? 

172^2  =  ? 

136^4  =  ? 

195-^3  =  ? 

138-^2  =  ? 

180-4  =  ? 

138^3  =  ? 

?    -f-2  =  ? 

• 

?    -v-4  =  ? 

?    -3  =  ? 

4 


DIVISION.     U.S.   POSTAL    SERVICE  77 

110.  All  mailable  matter  for  transmission  by  the  United  States 
mails  within  the  United  States  or  to  Cuba,  Mexico,  Hawaii,  Porto 
Rico,  Canada,  and  the  Philippine  Islands  is  divided  into  four 
classes :  first-,  second-,  third-,  and  fourth-class  matter. 

First-class  matter  includes  letters,  postal  cards,  and  anything 
sealed  or  otherwise  closed  against  inspection.  The  rate  for  first- 
class  m'atter  is  2/  per  ounce  or  fraction  thereof;  for  a  postal 
card,  1  / ;  for  a  reply  postal  card,  2  /.  Written  or  typewritten 
matter  is  of  the  first  class,  whether  sealed  or  unsealed. 

Second-class  matter  includes  newspapers  and  periodicals  entirely 
in  print.  When  sent  by  publishers  or  news  agents,  the  rate  is 
1  /  per  pound  or  fraction  thereof ;  when  sent  by  others,  1  /  for 
each  4  oz.  or  fraction  thereof. 

Third-class  matter  includes  books  and  catalogues  (weighing 
8  oz.  or  less),  circulars,  pamphlets,  proof  sheets  and  manuscript 
copy  accompanying  the  same,  and  engravings.  The  rate  is  1/ 
for  each  2  oz.  or  fraction  thereof.     The  limit  of  weight  is  4  lb. 

All  postal  matter  of  the  first,  second,  or  third  class  may  be 
registered  at  the  rate  of  10/  for  each  package  in  addition  to  the 
regular  rates  of  postage. 

The  rates  on  special  delivery  letters  are  10  /  per  letter  in  addition 
to  the  regular  postage.  Any  matter  on  which  a  special  delivery 
stamp  is  affixed  is  entitled  to  special  delivery  within  certain  limits. 

Foreign  rates  of  postage  are  as  follows :  letters,  5  /  per  ounce  for 
the  first  ounce,  and  3  /  for  each  additional  ounce.  (Double  rate 
is  charged  at  delivery  office  for  any  deficiency  in  prepayment.) 
Postal  cards,  2/  each;  newspapers  and  other  printed  matter, 
1/  for  2  oz. 

Some  foreign  countries,  as  Germany  and  Great  Britain,  come 
under  the  letter  rate  of  2/  per  ounce. 

All  fourth-class  matter  is  now  included  in  the  domestic  parcel 
post,  by  a  law  which  became  effective  January  1,  1913.  The  fol- 
lowing are  some  of  the  principal  features  of  this  law : 

The  country  is  divided  into  zones,  the  rate  of  postage  being  dependent  on 
the  zone  where  the  parcel  is  to  be  delivered.  The  zone  center  is  the  point 
of  mailing.     Regular  postage  stamps  are  used  on  parcel-post  packages. 


78 


PEACTicAL  busi:ness  aeithmetic 


Parcels  weighing  4  oz.  or  less  are  mailable  at  the  rate  oi  If  for  each 
ounce  or  fraction  of  an  ounce,  regardless  of  distance.  Parcels  weighing 
more  than  4  oz.  are  mailable  at  the  pound  rates  shown  in  the  table,  a 
fraction  of  a  pound  being  considered  as  a  full  pound. 

Books  and  catalogues  weighing  in  excess  of  8  oz.  may  be  sent  by  parcel  post. 

The  weight  limit  for  zones  1  and  2  is  50  lb. ;  for  all  the  other  zones,  20  lb. 

The  local  rate  applies  to  parcels  to  be  delivered  at  the  office  of  mailing, 
or  on  a  rural  route  starting  from  that  office. 

A  parcel  may  be  insured  against  loss  to  the  amount  of  its  actual  value 
not  exceeding  $50. 

A  special  delivery  of  a  parcel  will  be  made  on  the  payment  of  an  addi- 
tional 10)2^,  at  the  mailing  office. 

In  the  table,  the  rates  are  complete  up  to  11  lb.  From  this  point  on  only 
illustrative  weights  and  rates  are  given ;  omissions  are  indicated  by  stars. 

The  local  post  office  can  furnish  a  parcel-post  map  of  the  United  States 
showing  the  regions  included  in  the  different  zones. 


50  mi. 

so- 
ldo mi. 

150- 
300  mi. 

300- 
600  mi. 

600- 
1000  mi. 

lOOO- 
1400mi. 

1400- 
1800  mi. 

All  over 
1800  mi. 

First  Zone 

Second 
Zone 
Rate 

Third 
Zone 
Rate 

Fourth 
Zone 

RATE 

Fifth 
Zone 
Rate 

Sixth 
Zone 
Rate 

Seventh 
Zone 
Rate 

Eighth 

Weight 

Local 
Rate 

Zone 
Rate 

Zone 
Rate 

lib. 

$0.05 

$0.05 

$0.05 

$0.06 

$0.07 

$0.08 

$0.09 

$0.11 

$0.12 

21b. 

.06 

.06 

.06 

-.08 

.11 

.1.4 

.17 

.21 

.24 

31b. 

.06 

.07 

.07 

.10 

.15 

.20 

.25 

.31 

.36 

41b. 

.07 

.08 

.08 

.12 

.19 

.26 

.33 

.41 

.48 

51b. 

.07 

.09 

.09 

.14 

.23 

.32 

.41 

.51 

.60 

61b. 

.08 

.10 

.10 

.16 

.27 

.38 

.49 

.61 

.72 

71b. 

.08 

.11 

.11 

.18 

.31 

.44 

.57 

.71 

.84 

81b. 

.09 

.12 

.12 

.20 

.35 

.50 

.65 

.81 

.96 

91b. 

.09 

.13 

.13 

.22 

.39 

.56 

.73 

.91 

1.08 

101b. 

.10 

.14 

.14 

.24 

.43 

.62 

.81 

1.01 

1.20 

111b. 

.10 

.15 

.15 

.26 

.47 

.68 

.89 

1.11 

1.32 

*  *  * 

*  *  * 

*  *  * 

*  *  * 

*  *  * 

*  *  * 

*  *  * 

*  *  * 

*  *  * 

*  *  * 

151b. 

.12 

.19 

.19 

.34 

.63 

.92 

1.21 

1.51 

1.80 

*  *  * 

*  *  * 

*  *  * 

*  *  * 

*  *  * 

*  *  * 

*  *  * 

*  *  * 

*  *  * 

*  *  * 

201b. 

.15 

.24 

.24 

.44 

.83 

1.22 

1.61 

2.01 

2.40 

*  *  * 

*  *  * 

*  *  * 

*  *  * 

301b. 

.20 

.34 

.34 

*  *  * 

*  *  * 

*  *  * 

*  *  * 

401b. 

.25 

.44 

.44 

*  *  * 

*  *  * 

*  *  * 

*  *  * 

501b. 

.30 

.54 

.54 

DIVISION.     U.   S.   POSTAL    SEKVICE 


79 


ORAL    EXERCISE 

1.  What  is  the  postage  on  a  letter  weighing  1-  oz.  ?  4J  oz.  ? 
11  oz.?  3^oz.?  2^oz.?  41  oz.? 

2.  What  will  be  the  cost  of  postage  on  the  following  articles  at 
your  post  office  to  points  within  the  United  States :  an  ordinary 
letter  weighing  2|  oz. ;  a  registered  letter  weighmg  1 J  oz. ;  a 
bundle  of  papers  weighing  10  oz.  ? 

3.  Find  the  total  cost  of  postage  on  the  following  to  pomts 
within  the  United  States:  a  special  delivery  letter  weighing  li  oz.; 
some  printers'  proofs  weighing  18  oz. ;  some  separate  matter  for 
the  printer  weighing  12  oz. ;  a  pamphlet  weighing  6  oz. 

4.  Use  a  zone  map  and  find  the  cost  of  mailing  each  of  the 
following  articles : 


Article 

Weight 

Destination 

A  pair  of  opera  glasses 

21b.    80Z. 

Kansas  City,  Mo. 

A  pair  of  ladies'  gloves 

60Z. 

Indianapolis,  Ind. 

A  copy  of  Star-Land 

lib.     80Z. 

Macon,  Ga. 

A  copy  of  Whittier's  Poems 

1  lb.  12  OZ. 

Pittsburgh,  Pa. 

A  copy  of  Lowell's  Poems 

1  lb.  10  OZ. 

Denver,  Colo. 

A  box  of  merchandise 

31b.    80Z. 

Chicago,  111. 

A  box  containing  a  pair  of 

shoes 

3  lb.    6  OZ. 

Austin,  Tex. 

A  piece  of  hardware 

6  lb.    9  oz. 

Detroit,  Mich. 

5.  A  publisher  sends  20,000  copies  of  his  magazine  by  mail. 
If  each  magazine  and  wrapper  weighs  14i  oz.  and  the  total 
number  is  weighed  at  the  post  office  in  bulk,  what  will  the 
publisher  have  to  pay  for  postage  ? 

6.  A  subscriber  mailed  two  copies  of  the  above  magazine  to  a 
friend.    What  was  the  cost  for  postage  ? 

7.  25,000  copies  of  a  monthly  magazine  weighing  14i  oz.  were 
sent  by  mail.    What  was  the  cost  to  the  publisher  for  postage  ? 

8.  Find  the  total  cost  for  mailing  the  following:  printers' 
proof  weighing  18^  oz. ;  manuscript  and  printers'  proof  in  one 
package,  weighing  28i  oz. ;  a  special  delivery  letter,  weighing  |  oz. 


80  PEACTICAL   BUSINESS   AEITHMETIC 

PEICE   LISTS   AND   INVENTOEIES 

Price  Lists 

These  price  lists  are  to  he  used  in  making  out  the  inventories 
which  are  found  on  the  four  pages  following : 


Article 

1. 

2. 

3. 

4. 

Bedsteads 

$6.25 

$8.50 

111.75 

$5.25 

Bookcases 

42.00 

38.00 

25.00 

35.00 

Bureaus 

18.50 

27.25 

22.50 

16.50 

Cabinets : 

China 

22.00 

20.00 

27.50      - 

32.50 

Medicine 

2.25 

1.75 

2.50 

3.25 

Music 

10.00 

11.00 

9.00 

8.50 

Parlor 

25.50 

•     21.50 

25.00 

36.50 

Chairs : 

Easy 

12.50 

10.50 

15.00 

22.25 

Morris 

10.50 

12.25 

12.00 

9.75 

Piano 

5.00 

6.50 

7.25 

9.00 

Typewritel- 

3.50 

4.50 

4.00 

5.50 

Cheval  Mirrors 

20.00 

17.25 

18.50 

16.50 

Chiffoniers 

24.00 

18.20 

31.75 

27.50 

Davenports 

62.50 

50.00 

60.00 

45.50 

Desks  : 

Flat-top 

21.20 

17.60 

16.80 

22.30 

Roll-top 

23.50 

21.25 

25.50 

27.25 

Typewriter 

11.25 

12.25 

14.25 

10.25 

Dinner  Trays 

5.50 

6.25 

7.25 

5.25 

Footrests 

1.75 

1.50 

1.60 

2.00 

Hall  Racks 

14.25 

13.50 

17.25 

18.50 

Lounges 

25.00 

17.50 

21.50 

32.00 

Mattresses 

11.40 

12.50 

13.25 

17.50 

Ottomans 

5.25 

4.50 

4.25 

5.50 

Parlor  Suites 

63.00 

52.50 

75.00 

67.50 

Pillows 

2.50 

3.00 

3.50 

2.00 

Sideboards 

60.00 

50.00 

45.00 

37.50 

Tables : 

Dining 

21.50 

17.50 

22.50 

24.50 

Dressing 

37.50 

32.25 

21.50 

35.25 

Serving 

13.50 

11.00 

14.50 

10.50 

Work 

10.00 

9.25 

9.00 

10.25 

Wardrobes 

20.50 

25.25 

15.50 

21.75 

Washstands 

6.00 

7.50 

5.50 

8.00 

Each  inventory  may  be  worked  owt  jim  times,  using  the  above  price  lists. 
This  work  may  be  done  by  copying  the  data  and  making  the  extensions,  or  by 
making  the  extensions  only  and  then  totaling  each  inventory. 


WRITTEN  REVIEW 


81 


Inventories 


7  Bureaus 
19  Bedsteads 

12  Chifeoniers 

5  Dressing  Tables 
21  Washstands 

8  Mattresses 
23  Pillows 

6  Bookcases 

3  Davenports 

13  Lounges 

17  Easy  Chairs 

7  Morris  Chairs 
5  Parlor  Suites 

8  Music  Cabinets 

12  Piano  Chairs 
15  Parlor  Cabinets 

5  Sideboards 

13  Dining  Tables 

8  China  Cabmets 

4  Serving  Tables 

9  Work  Tables 
12  Dinner  Trays 

4  Medicine  Cabinets 

8  Wardrobes 

11  Cheval  Mirrors 
15  Ottomans 

12  Footrests 

5  Hall  Racks 

6-  Roll-top  Desks 
3  Flat-top  Desks 

9  Typewriter  Desks 
8  Typewriter  Chairs 


8  Bureaus 

17  Bedsteads 

15  Chiffoniers 

3  Dressing  Tables 

18  Washstands 

11  Mattresses 
21  Pillows 

5  Bookcases 

4  Davenports 

12  Lounges 

20  Easy  Chairs 

3  Morris  Chairs  , 

6  Parlor  Suites 

10  Music  Cabinets 

11  Piano  Chairs 

21  Parlor  Cabinets 
2  Sideboards 

16  Dining  Tables 

5  China  Cabinets 

6  Serving  Tables 

7  Work  Tables 
15  Dinner  Trays 

8  Medicine  Cabmets 

5  Wardrobes 

14  Cheval  Mirrors 

12  Ottomans 

17  Footrests 

7  Hall  Racks 

4  Roll-top  Desks 
2  Flat-top  Desks 

10  Typewriter  Desks 

6  Tjrpewriter  Chairs 


82 


PEACTICAL   BUSINESS   AEITHMETIC 


3. 

8  Bureaus 

15  Bedsteads 
14  Chiffoniers 

4  Dressing  Tables 
19  Washstands 

12  Mattresses 

18  Pillows 

8  Bookcases 

5  Davenports 

16  Lounges 
22  Easy  Chairs 

6  Morris  Chairs 

7  Parlor  Suites 

11  Music  Cabinets 
14  Piano  Chairs 

12  Parlor  Cabinets 

6  Sideboards 

10  Dining  Tables 

7  China  Cabinets 

6  Serving  Tables 

8  Work  Tables 

11  Dinner  Trays 

7  Medicine  Cabinets 

9  Wardrobes 

13  Cheval  Mirrors 

19  Ottomans 

12  Footrests 

6  Hall  Racks 

8  Roll-top  Desks 
4  Flat-top  Desks 

14  Typewriter  Desks 
10  Typewriter  Chairs 


4. 

9  Bureaus 
13  Bedsteads 

11  Chiffoniers 

7  Dressing  Tables 

17  Washstands 
9  Mattresses 

23  Pillows 

6  Bookcases 

3  Davenports 
21  Lounges     . 

18  Easy  Chairs 

9  Morris  Chairs 

4  Parlor  Suites 

9  Music  Cabinets 

13  Piano  Chairs 
18  Parlor  Cabinets 

4  Sideboards 

12  Dining  Tables 
9  China  Cabinets 

5  Serving  Tables 
11  Work  Tables 

14  Dinner  Trays 

5  Medicine  Cabinets 

7  Wardrobes 

17  Cheval  Mirrors 

15  Ottomans 

18  Footrests 

3  Hall  Racks 

5  Roll-top  Desks 

6  Flat-top  Desks 

11  Typewriter  Desks 

7  Typewriter  Chairs 


WRITTEN  EEVIEW 


83 


12  Bureaus 
23  Bedsteads 

13  Chiffoniers 

8  Dressing  Tables 

16  Washstands 

14  Mattresses 
22  Pillows 

4  Bookcases 
4  Davenports 

17  Lounges 

14  Easy  Chairs 
12  Morris  Chairs 

10  Parlor  Suites 
14  Music  Cabinets 
17  Piano  Chairs 
22  Parlor  Cabinets 

7  Sideboards 
14  Dining  Tables 

4  China  Cabinets 

11  Serving  Tables 

5  Work  Tables 

19  Dinner  Trays 

6  Medicine  Cabinets 

12  Wardrobes 

20  Cheval  Mirrors 

11  Ottomans 

21  Footrests 

4  Hall  Racks 

12  Roll-top  Desks 

5  Flat-top  Desks 

13  Typewriter  Desks 
12  Typewriter  Chairs 


6. 

14  Bureaus 
21  Bedsteads 
'  16  Chiffoniers 
11  Dressing  Tables 

14  Washstands 

15  Mattresses 

17  Pillows 

7  Bookcases 

7  Davenports 
19  Lounges 

25  Easy  Chairs 

11  Morris  Chairs 
9  Parlor  Suites 

12  Music  Cabinets 
21  Piano  Chairs 

16  Parlor  Cabinets 
9  Sideboards 

18  Dining  Tables 

6  China  Cabinets 
9  Serving  Tables 

10  Work  Tables 

13  Dinner  Trays 

10  Medicine  Cabinets 

15  Wardrobes 

16  Cheval  Mirrors 

19  Ottomans 

14  Footrests 

8  Hall  Racks 

9  Roll-top  Desks 
8  Flat-top  Desks 

7  Typewriter  Desks 

15  Typewriter  Chairs 


84 


PEACTICAL   BUSINESS   AEITHMETIC 


19  Bureaus 

21  Bedsteads 
11  Chiffoniers 

9  Dressing  Tables 

15  Washstands 

11  Mattresses 
24  Pillows 

9  Bookcases 
6  Davenports 

22  Lounges 

12  Easy  Chairs 

8  Morris  Chairs 

9  Parlor  Suites 
14  Music  Cabinets 

9  Piano  Chairs 
17  Parlor  Cabinets 

3  Sideboards 

13  Dining  Tables 

4  China  Cabinets 
11  Serving  Tables 
13  Work  Tables     - 
24  Dinner  Trays 

6  Medicine  Cabinets 

13  Wardrobes 

14  Cheval  Mirrors 

6  Ottomans 

8  Footrests 
11  Hall  Racks 

3  Roll-top  Desks 

7  Flat-top  Desks 

16  Typewriter  Desks 

9  Typewriter  Chairs 


8. 

17  Bureaus 

20  Bedsteads 
16  Chiffoniers 

6  Dressing  Tables 

21  Washstands 

15  Mattresses 
25  Pillows 
10  Bookcases 

2  Davenports 

16  Lounges 

8  Easy  Chairs 
13  Morris  Chairs 

3  Parlor  Suites 
10  Music  Cabinets 

7  Piano  Chairs 

22  Parlor  Cabinets 
5  Sideboards 

9  Dining  Tables 

10  China  Cabinets 
7  Serving  Tables 

17  Work  Tables 
21  Dinner  Trays 

9  Medicine  Cabinets 

11  Wardrobes 

18  Cheval  Mirrors 
9  Ottomans 

10  Footrests 

12  Hall  Racks 

2  Roll-top  Desks 
9  Flat-top  Desks 

10  Typewriter  Desks 

11  Typewriter  Chairs 


\ 


CHAPTER  VIII 

AVERAGE 
ORAL  EXERCISE 

1.  A  earns  $  3,  B  earns  $  4,  and  C  earns  $  5  per  day.  What 
do  the  three  earn  in  1  da.?  If  $12  were  paid  to  these  men  in 
equal  parts,  how  much  would  each  receive  ? 

2.  What  sum  is  intermediate  between  6,  7,  and  8  ?  between 
6,  8,  and  10  ?  between  6,  12,  and  18  ? 

111.  The  process  of  finding  a  number  that  is  intermediate 
between  two  or  more  other  numbers  is  called  average. 

112.  Example.  What  is  the  average  weight  of  3  bales  of 
cotton  weighing  460,  449,  and  475  lb.,  respectively? 

Solution.     The  aggregate  of  the  3  bales  of  cotton  is  1384  lb. 
1384  lb.  divided  into  three  equal  parts  shows  the  mean  or  average  449 

weight  to  be  4611  lb.  475 

To  find  the  average  of  consecutive  numbers,  add  the  highest  3"\J384 
number  to  the  lowest,  and  divide  by  2.  r^  ^ 

o 

WRITTEN  EXERCISE 

1.  A  tapering  board  is  14  in.  wide  on  one  end  and  18  in. 
on  the  other.     What  is  the  average  width  of  the  board? 

2.  A  manufacturing  pay  roll  shows  that  15  hands  are  em- 
ployed at  il.25  per  day,  12  hands  at  81.75  per  day,  16  hands 
at  12.25  per  day,"  32  hands  at  12.50  per  day,  and  5  hands  at 
16.50  per  day.     Find  the  average  daily  wages. 

3.  A  merchant's  sales  for  a  year  were  as  follows :  January, 
$12,156;  February,  $14,175;  March,  116,152;  April,  112,175 ; 
May,  112,465.95;  June,  112,476.05  ;  July,  115,145.40  r  August, 
112,431.46;  September,  117,245.90;  October,  $18,256.45; 
November,  $19,250.65;  December,  $19,654.20.  What  were 
his  average  sales  per  month? 

86 


86 


PRACTICAL   BUSINESS   ARITHMETIC 


4.  In  a  certain  school  of  300  pupils,  85  are  14  yr.  of  age ; 
50,  15  yr.  of  age ;  25,  16  yr.  of  age ;  75,  17  yr.  of  age ;  50, 
18  yr.  of  age;  15,  19  yr.  of  age.  What  is  the  average  age  of 
the  school? 

5.  The  attendance  for  a  certain  school  for  a  week  was  as  fol- 
lows :  Monday,  727  pupils  ;  Tuesday,  732  pupils  ;  Wednesday, 
756  pupils ;  Thursday,  761  pupils  ;  Friday,  734  pupils.  What 
was  the  average  daily  attendance  for  the  week  ? 

6.  What  should  a  ground  feed  made  from  50  bu.  of  oats 
worth  38^  per  bushel,  30  bu.  of  barley  worth  ISj^,  and  60 
bu.  of  corn  worth  69^  sell  for  in  order  to  make  10^  per 
bushel  on  each  ingredient  used  to  make  the  mixture  ? 

7.  Find  the  aggregate  weight  and  the  average  weight  per 
box  of  100  bx.  of  cheese  weighing  Q.%  64,  62,  60,  61,  65,  62,  64, 

61,  62,  61,  60,  60,  61,  62,  60,  68,  Q5,  6Q,  64,  62,  61,  6.%  6Q,  62, 

64,  67,  58,  62,  59,  59,  60,  62,  64,  66,  67,  58,  60,  65,  58,  62,  69, 

62,  65,  68,  69,  61,  65,  62,  61,  65,  68,  59,  62,  64,  58,  62,  65,  71, 
70,  58,  67,  58,  62,  64,  58,  62,  64,  65,  69,  65,  65,  62,  64,  60,  60, 

65,  60,  65,  65,  62,  60,  62,  64,  60,  72,  64,  70,  61,  62,  60,  60,  59, 
65,  60,  70,  58,  62,  61,  64  lb.,  respectively. 

8.  Counting  8  hr.  to  a  day,  find  the  total  amount  and  the 
average  daily  wages  in  the  following  contractor's  time  sheet  : 


Time   Sheet   for   Week   Ending  June 


Name 

M. 

T. 

w. 

T. 

F. 

s. 

Hours 

Days 

Daily 
Wages 

A MO TNT 

C.  E.  Ames 

8 

8 

8 

8 

8 

8 

$1.75 

W.  0.  Bye 

9 

10 

9 

10 

10 

8 

2.00 

M.  E.  Carey 

10 

9 

9 

10 

8 

10 

2.00 

W.  D.  Frey 

6 

8 

9 

10 

7 

8 

2.25 

G.  W.  Jones 

10 

10 

10 

8 

10 

8 

2.25 

D.  0.  Munn 

4 

4 

4 

6 

8 

6 

2.50 

E.  H.  Post 

6 

6 

6 

6 

4 

4 

3.00 

L.  C.  Roe 

10 

10 

10 

10 

4 

4 

3.25 

J.  H.  Small 

6 

8 

8 

10 

12 

12 

3.25 

H.  M.  Young 

8 

8 

8 

8 

8 

8 

3.50 

Total 

CHAPTER  IX 

CHECKING  RESULTS 

113.  It  has  been  seen  in  the  preceding  exercises  on  statis- 
tics, time  sheets,  etc.,  that  various  ruled  forms  provide  for  prac- 
tical and  convenient  methods  of  checking  results.  While-  it  is 
possible  to  give  a  great  variety  of  these  problems  it  is  also 
necessary  to  give  a  great  many  problems  that  do  not  furnish 
such  a  check. 

114.  It  is  very  important  that  all  results  be  checked.  The 
most  common  methods  of  checking  addition,  subtraction,  and 
division  have  already  been  mentioned.  Multiplication  may 
be  proved  by  dividing  the  product  by  either  factor,  or  as 
explained  on  page  52. 

The  properties  of  9  and  11  may  also  be  applied  to  advan- 
tage in  checking  results,  especially  results  in  multiplication  and 
division. 

PROPERTIES   OF   9   AND   11 

Properties  of  9 

115.  Any  number  of  lO's  is  equal  tg  the  same  number  of  9's 
plus  the  same  number  of  units ;  any  number  of  lOO's  is  equal 
to  the  same  number  of  99's  plus  the  same  number  of  units ; 
any  number  of  lOOO's  is  equal  to  the  same  number  of  999's 
plus  the  same  number  of  units ;  and  so  on. 

Thus,  10  =  one  9  +  1 ;  40  =  four  9's  +  4 ;  100  =  one  99  +  1 ;  300  = 
three  99's  +  3 ;  500  =  five  99's  +  5. 

116.  Any  number  may  be  resolved  into  one  less  than  as  many 
multiples  of  10  as  it  contains  digits. 

Thus,  946  =  900  +  40  +  6 ;  42175  =  40000  +  2000  +  100  +  70  +  5. 

87 


88  PRACTICAL   BUSINESS  ARITHMETIC 

117.  The  excess  of  9's  in  any  power  of  10  or  in  any  multiple 
of  a  power  of  10  is  the  same  as  the  significant  figure  (unless  that 
figure  is  9,  then  there  is  no  excess)  in  that  number.     Hence, 

The  excess  of  O's  in  any  number  is  equal  to  the  excess  of  9*s  in 
the  sum  of  its  digits. 

Thus,  the  excess  of  9's  in  241  =2  +  4  +  1,  or  7.  The  excess  of  9's  in 
946  =  9  +  4  +  6,  or  19;  but  19  contains  9,  and  the  excess  of  9's  in  19  =  1  + 
9,  or  10;  hut  10  contains  9,  and  the  excess  of  9's  in  10  =  1  +  0,  or  1;  the 
excess  of  9's  in  946  is  therefore  shown  to  be  1. 

118.  In  finding  the  excess  of  9's  in  any  number,  omit  all  9's 
and  all  combinations  of  two  or  three  digits  which  it  is  seen  at 
a  glance  will  make  9  or  some  multiple  of  9. 

Thus,  in  finding  the  excess  of  9's  in  9458,  begin  at  the  left,  reject  the 
first  digit  9,  the  sum  of  the  next  two  digits,  9,  and  the  single  8  will  be  the 
excess  of  9's  in  the  entire  number. 

Properties  of  11 

119.  Any  number  of  lO's  is  equal  to  the  same  number  of  ll's 
minus  the  same  number  of  units;  any  number  of  lOO's  is  equal 
to  the  same  number  of  99's  plus  the  same  number  of  units  ;  any 
number  of  lOOO's  is  equal  to  the  same  number  of  lOOl's  minus 
the  same  number  of  units ;  and  so  on. 

Thus,  40  =  four  ll's  -  4;  500  =  five  99's  +  5;  7000  =  seven  lOOl's  -  7. 

120.  It  is  therefore  clear  that  even  powers  of  10  are  multiples 
of  11  plus  1  and  odd  powers  of  10  are  multiples  of  11  minus  1. 

Thus,  102  or  100  =  nine  ll's  +  1 ;  lO^  or  1000  =  ninety-one  ll's  -  1 ;  10* 
or  10,000  =  nine  hundred  nine  ll's  +  1. 

121.  From  the  foregoing  it  is  evident  that : 

The  excess  oflfs  in  any  number  is  equal  to  the  sum  of  the  digits 
in  the  odd  places  (increased  by  11  or  a  multiple  of  11  if  necessary') 
minus  the  sum  of  the  digits  in  the  even  places. 

Thus,  the  excess  of  ll's  in  45  is  1  (5  —  4)  ;  the  excess  of  ll's  in  125  is 
4  (5  -  2  +  \^^))  ;  the  excess  of  ll's  in  2473  is  9  (3  +  4  +  11  -  7+2  =  9); 
the  excess  of  ll's  in  14,206  is  5. 


D4»  = 

217  = 

8 

451  = 

0 

688  = 

6 

CHECKING  RESULTS  89 


Checking  Addition  and  Subtraction 

122.  Examples,  i.  By  casting  out  the  9's,  show  that  the 
sum  of  935,  651,  782,  and  465  is  2833. 

Solution.  The  sum  of  the  digits  in  935  is  17  ;  but  since  17  935  =  8 
contains  9,  find  the  sum  of  the  digits  in  17  and  the  result,  8,  is  the  (?c-i  _  o 
excess  of  9's  in  the  entire  number.  In  like  manner  find  the  ex- 
cess  of  9's  in  651,  782,  and  465.  Since  935  is  a  multiple  of  9  +  8,  '  ^"^  =  ^ 
651  a  multiple  of  9  +  3,  782  a  multiple  of  9  +  8,  465  a  multiple  of  465  =  6 
9  +  6,  the  sum  of  these  numbers,  2833,  should  equal  a  multiple  of  2833  =  7 
9  4-  (8  +  3  +  8  +  6),  or  9  +  25.  25  is  a  multiple  of  9  +  7,  and  2833 
is  a  multiple  of  9  +7  ;  hence,  the  addition  is  probably  correct. 

2.    By  casting  out  the  ll's,  show  that  the  sum  of  648,  217, 

451,  and  688  is  2004. 

Solution.  8-4  +  6-0  =  10,  the  excess  of  ll's  in  648. 
7Tri4.2^ro=8,  the  excess  of  ll's  in  217.  12  (11+  1)  -5  + 
4  — 0  =  11 ;  but  11  contains  11,  hence,  the  excess  of  IPs  in  451 
is  0.  8  -  8  +  6^^  =  6,  the  excess  of  ll's  in  688.  Since  648  is 
a  multiple  of  11  +  10,  217  a  multiple  of  11  +  8,  451  a  multiple  of 
11,  and  688  a  multiple  of  11  +  6,  the  sum  of  these  numbers,  2004,  2004  =  2 
should  be  a  multiple  of  11  +  (10  +  8+6),  or  11  +  24.  24  is  a 
multiple  of  11  +  2  and  2004  is  a  multiple  of  11  +  2;  hence,  the  addition  is 
probably  correct. 

123.  Subtraction  may  be  proved  either  by  casting  out  the  9's 
or  ll's  in  practically  the  same  manner  as  addition. 

The  difference  between  the  excess  of  9's  or  ll's  in  the  minuend  and  sub- 
trahend should  equal  the  excess  of  9's  or  ll's  in  the  remainder;  or  the  sum 
of  the  excess  of  9's  or  ll's  in  the  subtrahend  and  remainder  should  equal 
the  excess  of  9's  or  ll's  in  the  minuend. 

These  methods  are  but  little  used  for  checking  addition  and  subtraction. 
Addition  is  generally  checked  as  explained  on  page  20,  and  subtraction  as 
explained  on  page  32.  On  the  other  hand,  long  multiplications  and  divi- 
sions are  almost  always  checked  by  applying  the  properties  of  9  or  11. 

Checking  Multiplication  and  Division 

124.  Examples,     l.   By  casting  out  the  9's  show  that  the 

product  of  64  x  95  is  6080. 

Solution.    The  excess  of  9's  in  95  is  5,  and  in  64,  1.     Since  95  95  =  5 

is  a  multiple  of  9  +  5  and  64  a  multiple  of  9+1,  the  product  of  fiA_i 

64  X  95  should  be  a  multiple  of  9  plus  (1x5).     1  x  5  or  5  equals    —  ""  _ 

.  the  excess  of  9's  in  6080  ;  hence,  the  work  is  probably  correct.  6080  =  5 


90  PRACTICAL   BUSINESS   ARITHMETIC 

2.  By  casting  out  the  ll's  show  that  the  product  of  46  x  95 
is  4370. 

Solution.    The  excess  of  ll's  in  95  is  7,  and  in  46,  2.     Since  95  =  "J 

95  is  a  multiple  of  11  +  7  and  46  a  multiple  of  11  +  2,  the  prod-  Ar  —  0 

uct  of  46  X  95  should  be  a  multiple  of  11  plus  (2  x  7)  or  14;  but  -^77-  ~  - 

14  is  a  multiple  of  11  +  3.     Since  the  product  4370  is  a  multiple  of  4370  =  3 
11  +  3,  the  work  is  probably  correct. 

125.  Division  may  be  proved  either  by  casting  out  the  9's  or 
ll's  in  practically  the  same  manner  as  multiplication.  The 
excess  of  9's  or  ll's  in  the  quotient  multiplied  by  the  excess 
of  9's  or  ll's  in  the  divisor  should  equal  the  excess  of  9's  or 
ll's  in  the  dividend,  minus  the  excess  of  9's  or  ll's  in  the  re- 
mainder, if  any. 

Casting  out  the  9's  will  not  show  an  error  caused  by  a  transposition  of 
figures;  but  casting  out  the  ll's  will  show  such  an  error.  The  method  of 
casting  out  the  ll's  is  therefore  considered  the  better  proof. 

WRITTEN  EXERCISE 

1.  Determine  without  dividing  whether  82.64  is  the  quo- 
tient of  11375.44-521. 

2.  Determine  without  multiplying  whether  $1807.50  is  the 
product  of  482  times  $3.75. 

3.  Determine  without  adding  whether  4231  is  the  sum  of 
296,  348,  924,  862,  956,  and  845. 

4.  Multiply  34,125  by  729  in  two  lines  of  partial  products 
and  verify  the  work  by  casting  out  the  9's. 

5.  Find  the  cost  of  173,000  shingles  at  14.27  per  thousand, 
in  two  lines  of  partial  products,  and  verify  the  work  by  casting 
out  the  ll's. 

6.  Find  the  cost  of  126,000  ft.  of  clear  pine  at  124.60  per 
thousand,  in  two  lines  of  partial  products,  and  verify  the  work 
by  casting  out  the  9's. 

7.  Find  the  cost  of  2,191,000  ft.  of  flooring  at  $32.08  per 
thousand,  in  two  lines  of  partial  products,  and  verify  the  work 
by  casting  out  the  ll's. 


FRACTIONS 


CHAPTER   X 


DECIMAL  FRACTIONS 


ORAL  EXERCISE 

1.  In  the  number  17.62  what  figure  stands  for  the  dollars? 
the  tenths  of  a  dollar?  the  hundredths  of  a  dollar? 

2.  What  name  is  given  to  the  point  which  separates  the 
whole  number  of  dollars  from  the  part  of  a  dollar  ? 

3.  Read:  3.5  dollars;  3.5  ft.;  27.5  1b.;  .7  of  a  dollar;  .5 
of  a  ton;  16.6;  .9;  9.25  dollars;  7.25  ft.;  8.75  rd.;  .95  of  a 
dollar;  .85  of  a  pound  sterling  ;   .57. 

4.  What  is  the  first  place  at  the  right  of  the  decimal  point 
called  ?  the  second  place  ? 

5.  In  the  accompanying 
diagram  what  part  of  ^  is  ^  ? 
What  part  of  ^  is  (7?  What 
part  of  C  is  i>? 

6.  What  part  of  A  is  (7? 
What  part  of  ^  is  D? 

7.  If  J.  is  a  cubic  inch,  what  is  jB?   C?  i>? 

8.  In  a  pile  of  10,000  bricks  one  brick  is  what  part  of  the 
whole  pile?  10  bricks  is  what  part  of  the  whole  pile?  100 
bricks  is  what  part  of  the  whole  pile?  1000  bricks  is  what 
part  of  the  whole  pile  ? 

9.  How  may  one  tenth  be  written  besides  ^^q?  one  hun- 
dredth besides  y^^  ?  one  thousandth  besides  i-qq-q  ? 

126.  Units  expressed  by  figures  at  the  right  of  the  decimal 
point  are  called  decimal  units. 

127.  A  number  containing  one  or  more  decimal  units  is 
called  a  decimal  fraction  or  a  decimal. 

91 


92  PKACTICAL   BUSINESS   AKITIOIETIC 

IfOTATIOX  AND  XUMEKATIOy 
ORAL  KTIBCBgC 

1.  Read :  0.7 ;  0.03 ;  0.25.  How  manj  jdiftoeB  most  be  used 
to  express  completelj  any  number  of  hundredths? 

2.  Read:  0.004;  0.025;  0.725.  How  many  places  must  be 
used  to  express  (XMnj^^ely  any  number  of  thousandths? 

3.  Read:  .0005;  .00007;  .000009;  .0037;  .00045;  .000051; 
.0121;    .00876;    .000218;    .1127;    .01525;    .0O45S1;    .16067. 

4.  How  many  places  must  be  used  to  express  oompletely  any 
number  of  ten>thousandths?  any  numb^  of  hundred-thou- 
sandths? any  number  of  millionths? 

128.  In  leadmg  detwiate  pranoiiiiee  tiie  woid  mad  at  the 
dedmal  pmnt  and  omit  it  in  all  oth^r  j^bees. 


OUSOS  or  Mo  SMY  six  imtdredjhe 
say  «ur  kmmdnd  mdJoM 


The  relaticm  of  integers  and  decimals  with  their  increas- 
ii^  and  decreasing  orders  to  the  left  and  to  the  right  of  the 
deeimal  point  is  shown  in  the  f (blowing 

NuMEBATiox  Table 


I    4 


£     * 


98     7.      654,      321.234      667 

130.  Hundredths  are  frequently  referred  to  as  per  cent,  a 
phrase  originally  meaning  hy  tke  immdrwd* 

131.  The  symbol  %  stands  for  hundredUis  and  k  read  jMr«i9il. 
49%  =  .i5;  iS%Q{»uanlnr=.4SQfiL 


DECliMAL   FRACTIONS  93 

ORAL  EXERCISE 

Read  : 

1.  0.073.  5.  532.002.  9.  31.08%. 

2.  0.00073.  6.  60.0625.  10.  126.75%. 

3.  3004.025.  7.  63.3125.  ii.  2150.1875. 

4.  300.4025.  8.  126.8125.  12!  3165.00625. 

13.  131.3125  T.  15.    A  tax  of  1.0625  mills. 

14.  240.0125  A.  16.  A  tax  of  9.1875  mills. 

17.  Read  the  number  in  the  foregoing  numeration  table. 

18.  Read  the  following,  using  the  words  "  per  cent " :  .17; 
28;   .85;  .67;  .425;   .37 J. 

19.  Read  the  following  as  decimals,  not  using  the  words 
''percent":  25%;  75%;   87%;   62^  % ;  27.15%. 

20.  Read  aloud  the  following  : 

a.  The  value  of  a  pound  sterling  in  United  States  money  is 
84.8665. 

h.  A  meter  (metric  system  of  measures)  is  equal  to 
39.37079  in.;  a  kilometer,  to  0.62137  mi. 

c.  1  metric  ton  is  equal  to  1.1023  ordinary  tons ;  1.5  metric 
tons  are  equal  to  1.65345  ordinary  tons. 

d.  A  flat  steel  bar  3  in.  wide  and  0.5  in.  thick  weighs 
5.118  lb. 

e.  The  circumference  of  a  circle  is  3.14159  times  the  length 
of  its  diameter. 

WRITTEN   EXERCISE 

Write  decimally : 

1.  Five  tenths ;  fifty  hundredths ;  five  hundred  thousandths. 

2.  Nine  hundred  and  eleven  ten-thousandths  ;  nine  hundred 
eleven  ten-thousandths;    five  hundred  and  two  thousandths. 

3.  One  hundred  seventy-four  millionths;  one  hundred 
seventy-four  million  and  seven  millionths ;  seven  million  and 
one  hundred  seventy-four  millionths. 

4.  Seven  thousand  and  seventy-five  ten-thousandths;  two 
hundred  fifty-seven  ten-millionths ;  two  hundred  and  forty-six 
millionths ;  two  hundred  forty-six  millionths. 


94  PRACTICAL   BUSINESS  AEITHMETIC 

5.  Four  million  ten  thousand  ninety-seven  ten-millionths ; 
four  million  ten  thousand  and  ninety-seven  ten-millionths;  five 
hundred  millionths ;  five  hundred-millionths. 

6.  Six  hundred  six  and  five  thousand  one  hundred-thou- 
sandths; six  hundred  six  and  fifty-one  hundred-thousandths; 
fifty-six  and  one  hundred  twenty-eight  ten-billionths. 

7.  Seventeen  thousand  and  eighteen  hundred  seventy-six 
millionths ;  seventeen  thousand  and  eighteen  hundred  seventy- 
six  ten-thousandths ;  twenty-one  hundred  sixteen  hundredths. 

132.  In  the  number  2.57  there  are  2  integral  units,  5  tenths 
of  a  unit,  and  7  hundredths  of  a  unit.  In  the  number  2.5700 
there  are  2  integral  units,  5  tenths  of  a  unit,  7  hundredths  of 
a  unit,  0  thousandths  of  a  unit,  and  0  ten-thousandths  of  a  unit. 
2.5700  is  therefore  equal  to  2.57.     That  is. 

Decimal  ciphers  may  he  annexed  to  or  omitted  from  the  right 
of  any  number  without  changing  its  value. 

ORAL  EXERCISE 

Mead  the  following  (a)  as  printed  and  (h~)  in  their  simplest 
decimal  form : 

1.  0.700.  3.    16.010.  5.  0.50.  7.    0.7000. 

2.  5.2450.         4.    18.210.  6.  0.00950.  8.    12.9010. 

ADDITION 

ORAL  EXERCISE 

1.  What  is  the  sum  of  0.4,  0.05,  0.0065? 

2.  What  is  the  sum  of  0.3,  0.021,  0.008  ? 

3.  Find  the  sum  of  seven  tenths,  forty-four  hundredths,  and 
two;  of  four  tenths,  twenty-one  hundredths,  and  six  thou- 
sandths. 

133.  Example.    Find  the  sum  of  12.021,  256.12,  and  27.5. 

Solution.    Write  the  numbers  so  that  their  decimal  points  12.021 

stand  in  the  same  vertical  column.    Units  then  come  under  units,  ogg  1  o 
tenths  under  tenths,  and  so  on.    Add  as  in  integral  numbers  and  07c 

place  the  decimal  point  in  the  sum  directly  under  the  decimal  ' 


points  in  the  several  numbers  added.  295.641 


DECIMAL   FEACTIONS  95 

WRITTEN   EXERCISE 

Find  the  sum  of: 

1.  7.5,  165.83,  5.12T,  6.0015,  and  71.215. 

2.  257.15,  27.132,  5163,  8.000125,  and  4100.002. 

3.  0.175,  5.0031,  .00127,  70.2116001,  and  21.00725. 

4.  51.6275,  19.071,  0.000075,  21.00167,  and  40,000.01. 

5.  2.02157,  2.1785,  2500.00025,  157.2165,  and  7.0021728. 

6.  Copy,  find  the  totals  as  indicated,  and  check : 

$1241.50  19215.45  $1421.12  $1421.32  ? 

1.52  1275.92  1.46..  1618.40  ? 

349.21  3725.41  2.18  1920.41  ? 

2975.47  7286.95  7.96  10.20  ? 

27.14  8276.92  14.21  41.64  ? 

9218.49  7271.44  1240.80  126.18  ? 

5.17  8926.95  7216.80  24.17  ? 

12627.85  8972.76  4.75  240.20  ? 

721.92  7214.25  8.16  960.80  ? 

11.41  8142.76  .47  1860.45  ? 

1.21  8436.14  .92  9270.54  ? 

.72  8435.96  9.26  75.86  ? 

14178.21  7926.14  1490.75  45.95  ? 

2172.14  9214.72  1860.54  75.86  ? 

726.95  1241.16  9265.80  72.18  ? 

85.21  4214.71  625.50  9260.14  ? 

75.92  8726.19  240.75  1.20  ? 

72604.25  2140.12  60.50  7.40  ? 

124.61  7146.14  120.41  8.32  ? 

2114.62  7214.86  4101.08  2860.14  l_ 

?         ?  ?  ?  ? 

7.  Find  the  suni  of  twenty-one  hundred  sixty-five  and  one 
hundred  sixty-five  ten-thousandths,  thirty-nine  and  twelve 
hundred  sixty-five  millionths,  twenty-seven  hundred  thirty- 
six  and  one  millionth,  four  and  six  tenths,  six  hundred  and 
six  thousandths,  and  six  hundred  sixty-five  thousandths. 


96  PRACTICAL   BUSINESS   AKITHMETIG 

SUBTRACTION 

ORAL  EXERCISE 

1.  From  the  sum  of  0.7  and  0.4  take  0.5. 

2.  From  the  sum  of  0.07  and  0.21  take  0.006. 

3.  From  seventy-four  hundredths  take  six  thousandths. 

4.  To  the  difference  between  .43  and  .03  add  the  sum  of 
.45  and  .007. 

5.  Goods  on  hand  at  the  beginning  of  a  week,  $24.50; 
goods  purchased  during  the  week,  $35.50;  goods  sold  during 
the  week,  $36 ;  goods  on  hand  at  the  close  of  the  week,  $36.50. 
What  was  the  gain  or  loss  for  the  week? 

134.    Example.     From  14.27  take  5.123. 

Solution.     Write  the  numbers  so  that  the  decimal  points  stand         14.27 
in  the  same  vertical  column.     The  minuend  has  not  as  many  places  c  -i  oo 

as  the  subtrahend  ;  hence  suppose  decimal  orders  to   be  annexed  ' 

until  the  right-hand  figure  is  of  the  same  order,  then  subtract  as  t^'.-L^:! 

in  integers  and  place  the  decimal  point  in  the  remainder  directly  under  the 
decimal  points  in  the  numbers  subtracted. 

WRITTEN  EXERCISE 

Find  the  difference  between: 

1.  7.2154  and  2.8576.  5.    9  and  5.2675. 

2.  17.2157  and  1.0002.  6.    16  and  5.0000271. 

3.  1.0005  and  .889755.  7.    .0002  and  .000004. 

4.  $1265.45  and  $87.99.  8.    24.503  and  17.00021.- 
9.    The  sum  of  two  numbers  is  166.214.     If  one  of  the 

numbers  is  40.21,  what  is  the  difference  between  the  numbers? 

10.  The  minuend  is  127.006  and  the  remainder  15.494. 
What  is  the  sum  of  the  minuend,  subtrahend,  and  remainder? 

11.  From  the  sum  of  ninety-nine  ten-thousandths,  one  hun- 
dred lifty-one  and  five  thousandths,  two  hundred  fifty-two  and 
twenty-five  millionths,  six  tenths,  and  eighteen  and  one  hun- 
dred seventy-five  thousandths  take  the  sum  of  twelve  hundred 
fifteen  millionths,  and  one  hundred  eighty-eight  thousandths. 


DECIMAL   FRACTIONS  9V 

12.  From  the  sum  of  two  hundred  fifty-seven  thousandths 
and  eight  and  one  hundred  twenty-six  millionths  take  the  sum 
of  five  hundred  ten  thousandths  and  two  and  one  hundred 
twenty-four  ten-thousandths. 

13.  A  merchant  had,  at  the  beginning  of  a  year,  goods 
amounting  to  18165.95.  During  the  year  his  purchases 
amounted  to  $5265.90  and  his  sales  to  19157.65.  At  the  close, 
of  the  year  he  took  an  account  of  stock  and  found  that  the 
goods  on  hand  were  worth  17216.56.  What  was  his  gain  or 
loss  for  the  year  ? 

14.  A  provision  dealer  had  on  hand  Jan.  1,  goods  worth 
14127.60.  His  purchases  for  the  year  amounted  to  $4165.95 
and  his  sales  to  $6256.48.  Dec.  31  of  the  same  year  his  in- 
ventory showed  that  the  goods  on  hand  were  worth  $3972.50. 
If  the  amount  paid  for  freight  on  the  goods  bought  amounted 
to  $237.50,  what  was  his  gain  or  loss  on  provisions? 

15.  I  had  on  hand  Jan.  1,  lumber  amounting  to  $4210.60. 
During  the  year  my  purchases  amounted  to  $3126.50,  and  my 
sales  to  $4165.85.  I  lost  by  fire  lumber  valued  at  $506.75,  for 
which  I  received  from  an  insurance  company  $500.  Dec. 
31,  my  inventory  showed  the  lumber  to  be  worth  $5209.08. 
How  much  did  I  gain  or  lose  on  lumber  during  the  year? 

16.  At  the  beginning  of  a  year  my  resources  were  as  follows: 
cash  on  hand,  $1262.50;  goods  in  stock,  $1742.85;  account 
against  A.  M.  Eaton,  $146.50.  At  the  same  time  my  liabili- 
ties were  as  follows:  note  outstanding,  $156.85;  account  in 
favor  of  Robert  Wilson,  $521.22.  During  the  year  I  made  an 
additional  investment  of  $1250.65,  and  withdrew  for  private 
use  $275.  I  sold  for  cash  during  the  year  goods  amounting  to 
$1250.75,  and  bought  for  cash  goods  amounting  to  $530.90  ;  I 
also  paid  Robert  Wilson  $320  to  apply  on  account.  At  the 
close  of  the  year  my  inventory  showed  goods  in  stock  valued  at 
$750.48.  What  was  my  gain  or  loss  for  the  year  and  my  pres- 
ent worth  at  the  close  of  the  year  ? 

Do  not  fail  to  check  all  problems.  No  phase  of  arithmetic  is  more 
important. 


98  PRACTICAL  BUSINESS  ARITHMETIC 

MULTIPLICATION 

ORAL  EXERCISE 

1.  How  many  times  .4  is  4  ?  .77  is  7.7  ?  .999  is  9.99? 

2.  44  is  how  many  times  .44?  22  is  how  many  times  .022? 
1  is  how  many  times  .001  ?  .01  is  how  many  times  .0001  ? 

3.  Read  aloud  the  following,  supplying  the  missing  terms  : 
Removing  the  decimal  point   one   place   to   the    right   multi- 
plies  the  value  of  the  decimal  by ;  two  places, the 

value  by ;  three  places, the  value  by  . 

4.  Multiply  12.1252  by  1000  ;  by  100  ;  by  100,000. 

5.  Multiply  19.375  by  100  ;  by  10,000  ;  by  100,000. 

6.  Multiply  5.15  by  10;  by  100;  by  1000 ;  by  10,000. 

7.  Multiply  .000016  by  1000;  by  100,000 ;  by  1,000,000. 

8.  Multiply  167.50  by  10  ;  by  100  ;  by  1000  ;  by  10,000. 

9.  Multiply  .0037  by  10;  by  100;  by  1000;  by  10,000,000. 

10.  What  part  of  1  is  .1  ?  of  7  is  .7?  of  29  is  2.9? 

11.  What  part  of  84  is  .84?  of  129  is  1.29?  of  1275  is  12.75? 

12.  What  part  of  .6  is  .006  ?  of  .64  is  .0064? 

Read  aloud  the  following,  supplying  the  missing  terms : 
a.  Each  removal  of  the  decimal  point  one  place  to  the  left 
the  value  of  the  decimal  by  10. 


h.    To  divide  a  decimal  by is  to  find  one  tenth  (.1)  of 

it,  or  to it  by  .1. 

13.  Give  a  short  method  for  multiplying  a  number  by  .1 ;  by 
.01;  by  .001;  by  .0001. 

14.  Multiply  .009  by  .1;  by  .01;  by  .001. 

15.  Multiply  217.59  by  .1;  by  .01 ;  by  .001. 

16.  Multiply  54.65  by  .01;  by  .00001;  by  .000001. 

17.  Multiply  2.375  by  .1;  by  .01;  by  .001  ;  by  .0001. 

18.  Multiply  25.215  by  .1;  by  .01;  by  .001;  by  .0001. 

19.  Multiply  2111  by  .01  ;  by  .001 ;  by  .0001 ;  by  .00001. 

20.  Compare   2400  x  $0.06   with   100x24x10.06  or  with 
24  X  $6. 

21.  Compare  3000  x  612.251  with  1000  x  3  x  612.251,  or  with 
3  x  612251. 


DECIMAL  FRACTIONS  99 

22.  Multiply  21.25  by  2400. 

Solution.     2400  is  24  times  100.     Multiply  by  100  2125  2125 

"by  removing  the  decimal  point  two  places  to  the  right.                 qa  oj^ 

The  result  is  2125.     24  times  2125  equals  51,000,  the  -  ao^TT 

required  product.  ^^^^  ^^^^ 

In  multiplying  begin  with  either  the  lowest  or  the  4250  8500 

highest  digit  in  the  multiplier  as  shown  in  the  margin.  51000  51000 

23.  Formulate  a  brief  rule  for  multiplying  a  decimal  by  any 
number  of  lO's,  lOO's,  lOOO's,  etc. 

24.  Find  the  cost  of  : 

a.  500  lb.  at  18^.      d.    600  lb.  at  29^.      g,    900  lb.  at  34^. 

b.  150  1b.  at  14^.       e.    300  1b.  at  41^.      h.    700  1b.  at  51^. 

c.  200  lb.  at  26^.       /.    400  lb.  at  121^.    i.    1400  lb.  at  5^. 

135.   Examples,     l.   Multiply  41.127  by  4. 

Solution.  41.127  is  equal  to  41,127  thousandths.  41,127  thou-  41.127 
sandths  multiplied  by  4  equals  164,508  thousandths,  or  164. -508.    That  4 

is,  thousandths  multiplied  by  a  whole  number  must  equal  thousandths.    164.508 

2.    Multiply  41.127  by  .04. 

Solution.     The  multiplier,  .04,  is  equal  to  4  times.  01 ;  therefore,  41.127 

multiply  by  4  and  by  .01.    Multiplying  by  4,  as  in  problem  1,  the  qa 

result  is  164.508.    Multiplying  by  .01,  by  simply  moving  the  decimal  -i  nAcno 

point  in  the  product  two  places  to  the  left,  the  result  is  1.64508.  J-.o^OUo 

It  will  be  seen  that  the  number  of  deciiyial  places  in  the  product 
is  equal  to  the  decimal  places  in  the  multiplicand  and  multiplier. 

It  should  not  be  necessary  to  memorize  the  above  rule.  The  student 
should  know  at  a  glance  that  the  product  of  tenths  and  tenths  is  hundredths, 
of  tenths  and  hundredths  is  thousandths,  and  so  on. 

ORAL   EXERCISE 

1.  In  multiplying  24.05  by  3.14  can  you  tell  before  multiply- 
ing how  many  integral  places  there  will  be  in  the  product? 
how  many  decimal  places  ?     Explain. 

2.  How  many  integral  places  will  there  be  in  each  of  the  fol- 
lowing products  ;  2.5x4.015?  27.51x3.1416?  321.1  x 
201.51?  1.421x42.267?  126.5  x  .01?  1020x5.01?  .105x6? 
2.41  X  10.05  ?  How  many  decimal  places  will  there  be  in  each 
of  the  above  products  ? 


100 


PKACTICAL   BUSINESS  AKITHMETIC 


3.  What  are  400  bbl.  of  apples  worth  at  |2.12  per  barrel? 
at  11.27^^  per  barrel? 

4.  I  bought  60  lb.  of  sugar  at  8  0.04 J  and  gave  in  payment  a 
five-dollar  bill.     How  much  change  should  I  receive  ? 

5.  A  and  B  are  partners  in  a  manufacturing  business,  A  re- 
ceiving 52  %  and  B  48  %  of  the  yearly  profits.  The  profits  for 
a  certain  year  are  15000.  Of  this  sum  how  much  should  A  and 
B,  respectively,  receive  ? 


7.  2.531x31000. 

8.  .1724x18000. 

9.  .15539  X  2002. 


WRITTEN  EXERCISES 

Find  the  product  of  : 

1.  3.121x152.  4.  12.14x265. 

2.  3121  X  .152.  5.  9.004  x  .021. 

3.  31.21x15.2.  6.  . 3121  X. 0152. 

10.  A  man  owned  75%  of  a  gold  mine  and  sold  50%  of  his 
share.  What  is  the  remainder  worth  if  the  value  of  the  whole 
mine  is  $425,000? 

11.  A  man  bought  a  farm  of  240  A.  at  $137.50  per  acre. 
He  sold  75%  of  it  at  1 150  per  acre,  and  the  remainder  at  $175 
per  acre.     What  was  his  gain  ? 

12.  Copy  and  complete  the  following  table  of  statistics. 
Check  the  results.  (The  total  yield  multiplied  by  the  price 
per  bushel  should  equal  the  total  valuation.) 


Largest  Wheat-growing  States  in  a  Recent  Year 


State 

Yield  in  Bushels 

Farm  Price 
PER  Bushel 

Farm  Valuation 

North  Dakota 
Kansas 
Minnesota 
South  Dakota 

143,820,000 
92,290,000 
67,038,000 
52,185,000 

92.4^ 
92.4^ 
92.4^ 
92.4  j^ 

? 
? 
? 
? 

Total 

? 

9 

? 

13-15.    Make  and  solve  three  self-checking  problems  in  multi- 
plication of  decimals. 


DECIMAL   FRACTIONS  U<JI 


DIVISION 
ORAL  EXERCISE 

1.  Divide  by  8:  64  ft,  .64,  .064,  6.4. 

2.  Divide  by  9:  63  in.,  .63,  .063,  6.3. 

3.  Divide  by  16:  1640,  $6.40,  6.4,  .64,  .064. 

4.  Divide  by  15:  115.75,  17.50,  $0.75,  30.45,  3.045,  .3045. 

5.  Divide  337.5  by  45. 

7^ 

45)337.5 

315     =  45  times  7 
22.5  undivided 
22.5  =45  times  .5 
Check.    45  times  7.5  =  337.5 ;  hence,  the  work  is  correct. 

136.  In  the  above  exercise  it  is  clear  that  when  the  divisor  is 
an  integer^  each  quotient  figure  is  of  the  same  order  of  units  as  the 
right-hand  figure  of  the  partial  dividend  used  to  obtain  it. 

ORAL  EXERCISE 

1.  500  is  how  many  times  50?  175  is  how  many  times 
$7.50? 

2.  Divide  50  by  5 ;  500  by  50.  How  do  the  quotients 
compare  ? 

3.  Divide  7.50  by  15  ;  $75  by  150.  How  do  the  quotients 
compare  ? 

4.  720  is  how  many  times  72  ?     9  is  how  many  times  .9? 

5.  Divide  720  by  9;   72  by  .9;   7.2  by  .09;   .72  by  .009. 

137.  It  has  been  seen  that  multiplying  both  dividend  and 
divisor  by  the  same  number  does  not  change  the  quotient. 

138.  Therefore,  to  divide  decimals  when  the  divisor  is  not  an 
integer : 

Multiply  both  dividend  and  divisor  by  the  power  of  10  that 
will  make  the  divisor  an  integer,  ayid  divide  as  in  United  States 
money. 


I0£ 


PRACTICAL   BUSINESS   ARITHMETIC 


139.    Divide  0.3375  by  0.45. 

.3375  -f-  .45  =  33.75  -=-  45.     33.75  --  45  =  .7,  -with  a  remainder  of 
2.25.     2.25  -T-  45  =  .05.     The  quotient  is  therefore  .75. 

Observe  that  the  divisor  may  always  he  made  an  integer  if  the 
decimal  point  in  the  dividend  is  carried  to  the  right  as  many  places 
as  there  are  decimal  places  in  the  divisor. 

Should  there  be  a  remainder  after  using  all  the  decimal 
places  in  the  dividend,  annex  decimal  ciphers  and  continue  the  division 
as  far  as  i§  desired. 


.15 

45)33.75 
315 
2  25 
2  25 


Divide  : 

1.  1  by  1. 

2.  1  by  .1. 

3.  IbylO. 

4.  .Iby.l. 

5.  1  by  .01. 

6.  1  by  100. 

7.  1  by  .001. 

8.  .10  by  .10. 

9.  .01  by  .01. 

10.  1  by  1000. 

11.  1  by  .0001. 

12.  1  by  10,000. 

13.  1  by  .00001. 

14.  .001  by  .001. 

15.  1  by  100,000. 

16.  1  by  .000001. 

17.  .0001  by  .0001. 

18.  .00001  by  .00001. 


ORAL   EXERCISE 


19. 
20. 
21. 
22. 
23. 
24. 
25. 
26. 
27. 
28. 
29; 
30. 
31. 
32. 
33. 
34. 
35. 
36. 


33  by  .11. 
33  by  110. 
.33  by  .11. 
3.3  by  1.1. 
.0001  by  1. 
33  by  .011. 
33  by  1100. 
.0001  by  .1. 
3300  by  .11. 
330  by  .011. 
33  by  .0011. 
33  by  11000. 
.0001  by  .01. 
.033  by  .011. 
.0001  by  .001. 
.0033  by  .0011. 
.0001  by  .0001. 
.0001  by  .00001, 


Divide : 

1.  5842  by  .046.  6. 

2.  2.592  by  .108.  7. 

3.  1.750  by  8750.  8. 

4.  .00338  by  .013.  9. 


WRITTEN  EXERCISE 

2200  by  .44. 
231.6  by  579. 
950  by  19,000. 
81.972  by  .00009. 


11.  16  by  .0064. 

12..  1.86  by  31,000. 

13.  1600  by  64,000. 

14.  .0004  by  20,000. 


1.728  by  .0024.  lo.  115.814  by  .00079.  15.  100  by  .000001. 


DECIMAL  FRACTIONS 


103 


Find  the  sum  of  the  quotients  : 


16. 

17. 

18. 

8.1-J-.9. 

72  -H  8. 

125-250. 

81^.09. 

72-^.8. 

12.5-2.5. 

8.1 -f-. 09. 

7.2^.8. 

1.25 -=-2.5. 

.81-^900. 

72 -.08. 

12.5-250. 

.0081-9. 

.72 -.08. 

125  -^  2500. 

8.1^900. 

72 -.008. 

.125 --.025. 

810-^.009. 

72  -  8000. 

12500 -V-.  25. 

.0081-^9000.  . 

72 -.0008. 

125  ^  25000. 

81000^.009. 

.072 -.008. 

12500 -.025. 

81^.000009. 

72 -.00008. 

125  --  250000. 

8100  -  90000. 

.0072 -.0008. 

.  125 -r-.  00025. 

.00081 -^  90000. 

.00072^.00008. 

12500  ^  .0025. 

19. 

20. 

21. 

8.8-^2.2. 

17  -^  68. 

36-^.072. 

.88-^.22. 

1.7^6.8. 

3.6^.072. 

88 -^  .0022. 

.17-f-.68. 

.36^.072. 

8.8^2200." 

1.7^680. 

360 -5- .072. 

880  -V-  2200. 

170  -5-  680. 

.036 -.072. 

8.8 -f- 2.200. 

.017 -H- .068. 

3.6-72000. 

880^.2200. 

1.7-^68000. 

36  ^  720000. 

8800  -r-  2200. 

1700  --  6800. 

360 -.00072. 

880  -^  22000. 

1700  -  68000. 

3600 -.0072. 

880^.00022. 

.0017-^.0068. 

.0036^.0072. 

88000 -.0022. 

.00017^.00068. 

3.6^.000072. 

88000 -f-.  00022. 

.000017 -^  .000068. 

.00036^.00072. 

22.  The  produ 

ct  of  two  numbers  is  0.00025.  If  one  of  the 

numbers  is  0.0025,  what  is  the  other? 

23.  A  retailer  bought  450  yd.  of  cloth  for  11237.50  and 
sold  it  at  13.25  per  yard.     How  much  did  he  gain  per  yard? 

24.  A  drover  bought  a  flock  of  sheep  at  the  rate  of  13.30 
per  head.  He  sold  them  at  a  profit  of  $0.20  per  head  and 
received  $700.  How  many  sheep  were  there  in  the  flock 
and  what  was  his  gain  ? 


u 


CASL. 


104 


PRACTICAL   BUSINESS   ARITHMETIC 


25.    Copy   and  complete  the   following   table.      Check   the 
results. 

Largest  Oat-growing  States  in  a  Recent  Year 


State 

Yield  ix  Bushels 

Farm  Price 
I'ER  Bushel 

Farm  Valuation 

Illinois 
Iowa 

Wisconsin 
Minnesota 

? 
? 
? 
? 

81  <* 
31  j^ 

31^ 

54,818,000 
58,811,000 
27,119,000 
31,926,000 

Total 

? 

31/' 

? 

26-28.    Make    and    solve    three    self-checking    problems   in 
division  of  decimals. 

DIVIDING   BY  POWERS   AND   MULTIPLES   OF   TEN 

ORAL  EXERCISE 

1.  6.4  is  what  part  of  64?     $0.17  is  what  part  of  $1.70  ? 

2.  Compare  (as  in  problem  1)  $240.60  with  $24,060;  17.75 
ft.  with  1775  ft. 

3.  Compare  (as  in  problem  1)  .1  wdth  1;   .01  with  1;   .001 
with  1;  .0001  with  1. 

4.  Read  aloud  the  following,  supplying  the  missing  terms  : 

Removing  the    decimal  place   to   the   divides   the 

value  of  the  decimal  by  10  ;  two  places, tlie  value  of  the 

decimal  by  ;  three  places, the  value  of  the  decimal 

by . 

5.  Compare  the  quotient  of    28  ^  .7  with  the  quotient   of 


28  X  10  -7-  .7  X  10  ;  the  quotient  of  28  -t-  .7  with  the  quotient  of 
280  --  7. 

6.  Compare  the  quotient  of  16.4 -r- 40  with  the  quotient  of 
16.4  -5- 10  -f- 40-^10;  the  quotient  of  16.4  -^  40  with  the  quotient 
of  1.64  -J-  4.     What  is  the  quotient  of  56.77  divided  by  7000? 


.00811 


Solution.    Removing  the  decimal  point  three  places  to  the 
left  and  dropping  the  ciphers  of  the  divisor  is  equivalent  to  dividing 
both  dividend  and  divisor  by  1000  and  does  not  change  the  value     7^.05677 
of  the  quotient. 


DECIMAL  FRACTIONS  105 

Buying  and  Selling  by  the  Hundred 
oral  exercise 

1.  Compare  460  ^  100  x  $2  with  4.60  x  12. 

2.  Find  the  cost  of  450   lb.  of  guano  at  1 4  per  cwt. 

3.  Find  the  cost  of  600  lb.  of  wire  nails  at  34^  per  cwt. 

4.  Find  the  cost  of  4950  paving  stones  at  1 8  per  C. 

Solution.     C  stands  for  100.    4950  paving  stones  are  49.5  times  '*^'  ^ 

100  paving  stones.    Since  1  hundred  paving  stones  cost  $8,  49.5  8 

hundred  paving  stones  will  cost  49.5  times  ^8,  or  .'^396.  393  Q 

WRITTEN    EXERCISE 


Mnd  the  cost : 

Price  per 

Price  p 

QUANTFTY 

Hundredweight 

Quantity 

HUNDREDW 

1.    450  1b. 

55^ 

5. 

1600  lb. 

7V 

2.    510  1b. 

77^ 

6. 

2600  lb. 

15^ 

3.    640  1b. 

60^ 

7. 

4900  lb. 

70^ 

4.    330  1b. 

5Qff 

8. 

3100  lb. 

SS^ 

Buying  and  Selling  by  the  Thousand 
oral  exercise 


1.  Compare  3500  h-  1000  x  $^9  with  3.500  x  19. 

2.  Compare  12200  --  1000  x  $5  with  12.2  x  f  5. 

3.  Find  the  cost  of  7150  feet  of  lumber  at  111  per  M. 

Solution.     M  stands  for  thousand.     7150  feet  are  7.15  times  7.15 

1000  feet.    Since  1  thousand  feet  of  lumber  cost  $11,  7.15  thousand  11 

feet  will  cost  7.15  times  |11,  or  $78.65.  78^65 

Find  the  cost  of: 

4.  8500  tiles  at  18  per  M;  at  89  per  M. 

5.  4500  bricks  at  1 6  per  M  ;  at  $7  per  M. 

6.  7500  shingles  at  $12  per  M ;  at  §14  per  M. 

7.  3200  ft.  lumber  at  $14  per  M ;  at  $12  per  M. 

8.  15,000  ft.  lumber  at  111  per  M  ;  at  1 12  per  M. 

9.  12,000  ft.  lumber  at  1 16  per  M  ;  at  $15  per  M. 


106 


PRACTICAL   BUSINESS   ARITHMETIC 


WRITTEN    EXERCISE 

1.  Find  the  cost  of  17,500  shingles  at  |4  per  M. 

2.  What  is  the  cost  of  2700  envelopes  at  S2.25  per  M  ? 

3.  Find  the  cost  of  27,560  feet  of  oak  lumber  at  f  21  per  M. 

4.  Find  the  total  cost  of  : 


275  lb.  nails  at  $3.50  per  cwt. 
750  lb.  wire  at  13.75  per  cwt. 
750  lb.  guano  at  $4.75  per  cwt. 

9000  tiles  at  $9,375  per  M. 
2320  ft.  lumber  at  $23  per  M. 
1,270,500  bricks  at  $  6.75  per  M. 

4275  lb.  meal  at  $1.10  per  cwt. 
5600  lb.  feed  at  $1.10  per  cwt. 
5970  lb.  meal  at  $1.12  per  cwt.    500  lb.  oatmeal  at  $2.50  per  cwt. 

7.  Find  the  total  freight  on : 

8000  lb.  oil  at  70^  per  cwt.  4950  lb.  ale  at  52)^  per  cwt. 

1500  lb.  fish  at  58^  per  cwt.  9900  lb.  beef  at  72^  per  cwt. 

5100  lb.  salt  at  73 j^  per  cwt.  4950  lb.  pork  at  57^  per  cwt. 

8.  Find  the  amount  of  the  following  bill : 


125  bolts  at  $2.75  per  C. 
750  bolts  at  $3.50  per  C. 
450  fence  posts  at  $6  per  C. 

5.  Find  the  total  cost  of : 
7600  shingles  at  $4  per  M. 
14,400  ft.  plank  at  $9  per  M. 
24,560  bricks  at  $3.50  per  M. 

6.  Find  the  total  cost  of  : 
760  lb.  bran  at  $.60  per  cwt. 
5875  lb.  bran  at  $.70  per  cwt. 


^^^^-^^ 


.f9- 


.JL 


bought  of  ^McGraiv,   &  Id  ridge  dr  Go. 


y-T^orPC  7^  '^^.^."f-^^^^ ^?-^^^ 


zA 


(?  (?  <7  ~0-^.<^,-jry>r7-dy:^ ^--^--1(2.^^. 


/  l.r^i^ -J^.  ':&2^^^1^^^y^^  2y?  ^^^J?^/ 


c^c^(?  '^.^g:;3v^7f?7fi^^ /z-:^/^^t^ 


7-S'C>(?0 


2^ 


/^'-L^^7/: 


fT-CCC^ 


<i2Z2!:^iZ2 


■r 


J/--i6^?/^ 


DECIMAL  FRACTIONS 


107 


140.  The  accompanying  illustration  shows  the  three  dials  of 
a  gas  meter.  Each  division  on  the  dial 
at  the  right  denotes  100  cu.  ft.  of  gas 
consumed  ;  each  division  on  the  center 
dial  1000  cu.  ft. ;  and  each  division  on 
the  dial  at  the  left  10,000  cu.  ft.  The 
dials  are  read  from  left  to  right  by  simply 
taking  the  figures  which  the  hands  have 
just  passed  and  adding  two  ciphers  to  them. 

Thus,  the  above  dial  registers  20,000  cu.  ft.  +  5000  cu.  ft.  +  700  cu.  ft. 
=  25,700  cu.  ft. ;  but  it  is  only  necessary  to  write  257  (2,  5,  7)  and  add 
two  ciphers  to  get  this  result. 

WRITTEN  EXERCISE 

1.  Read  the  accompanying  meters  and  find  the  cost  of  the  gas 
consumed  during  the  period  Jan.  1  to  Feb.  1 
at  $1.20  per  1000  cu.  ft. 

2.  The  following  is  the  number  of  cubic 
feet  of  gas  used  in  a  residence  for  the  six 
months  ending  July  1 :  January,  2900 ; 
February,  3200;  March,  3700;  April,  2900  ; 
May,  2700;  June,  1200.  Find  the  total  gas 
bill  for  the  six  months  at  $0.90  per  1000 
cu.  ft. 

3.  Assuming  that  gas  is  worth  $0.95  per  1000  cu.  ft.,  find 
the  amount  of  the  following  bill,  less  10^. 


^v^o^is^^^    ^^^^us^^^ 


H  to  < 

to  *  1 
8 


g 


M^^ ,  2^^^ 


.-A-r^^ 


19- 


.rl^^^^?/^ 


To  The  Boston  Gas  and  Electric  Light  Co.,  Dr. 


For  Gas  supplied  by  meter 
— ^^/OO  cu.  h.  as  showTi  by  Meier  Dial 
■  /au  00  cu.  h.  as  shown  by  Meter  Dial  - 
— ^-^^iTOO  cu.  ft.  at  $1 .00  per  1 000  cu.  h. 

Discount  of  10%  allowed  if 
paid  P«  or  before 


c^.ta^,   19 


Received  payment  for         ^ 
the  Company 
-^^f^-  ^  19 


J  r£> 


j^\'  ^ 


/J 


108  PRACTICAL   BUSINESS   ARITHMETIC 

Buying  and  Selling  by  the  Ton  of  2000   Pounds 
oral  exercise 


1.  Compare  8000  -;-  2000  x  8  with  8000  -^  1000  x  4. 

2.  Compare  7000  --  2000  x  18  with  7x9. 

3.  Find  the  cost  of  4250  lb.  coal  at  1 8  per  ton. 

Solution.     4250  lb.  is  4.25  times  1000  lb.     If  the  cost  of  2  thou-  4.25 
sand  pounds  is  $8,  the  cost  of  1  thousand  pounds  is  $4.     Since  1 

thousand  pounds  of  coal  cost  $  4,  4.25  thousand  pounds  will  cost  4.25  4 

times  §4,- or  117.  17.00 

WRITTEN  EXERCISE 

1.    At  $9  per  ton,  find  the  cost  of  the  hay  in  the  following 
weigh  ticket.     Also  find  the  cost  at  88.75  per  ton. 


SCALES  OF  E.  H.  ROBINSON  &  CO. 
N0..2J22  y9y^^'  ^•'^■• 

From    y^K  yJA^J^^^T^^A^^  To_ 


Gross  .weight     Jj^  J^  / /O      lb. 

Tare      /  ^  ^  ^      Ih. 

Net  weight     Xa^jT^^^  1h 


3^^^=^^ 


Weigher 


2.    At  17.50  per  ton  find  the  cost  of  the  coal   in   the    fol- 
lowing weigh  ticket.     Also  find  the  cost  at  $6.95  per  ton. 


WELLINGTON ^WILD  COAL. CO, 

126  Main  Street,  Rochester,  N.Y. 

j-___  ~^  ^ 

Tenmaier  //Z^r^^i^^-y-?^  Received  h,j   t..lY\.  W rrXH/yx  h^<m. — ■ 


DECIMAL   FRACTIONS  109 

3.  What  will  8650  lb.  of  hay  cost  at  $12  per  ton? 

4.  Find  the  cost  of  2150  lb.  of  coal  at    $6    per    ton. 

5.  At  $32  per  ton,  what  is  the  cost  of  26,480  lb.  of 
phosphate  ? 

6.  Find  the  cost  of  54,260  pounds  of  coal  at  $5.80  per  ton. 

7.  Find  the  cost  of  12  loads  of  coal  weighing  4100,  3900, 
4306,  4100,  4060,  4300,  3286,  3980,  3850,  4130,  3700,  3950  lb. 
net,  at  15.20  per  ton. 

8.  Find  the  total  cost  of  :  5265  lb.  hard  coal  at  $8.40  per  ton ; 
12,200  lb.  soft  coal  at  $3  per  ton;  8275  lb.  cannel  coal  at $11.75 
per  ton;  34,160  lb.  egg  coal  at  $6.20  per  ton;  12,275  lb.  nut 
coal  at  $5.75  per  ton;  8753  lb.  grate  coal  at  $5.80  per  ton; 
24,160  lb.  stove  coal  at  $6.50  per  ton. 

9.  During  the  month  of  January,  in  a  recent  year,  there  were 
consumed  in  a  manufacturing  plant  72  loads  of  coal  weighing  as 
follows:  6100,  6500,  6700,  6840,  7210,  6680,  7250,  8400, 
6100,  6100,  6250,  6380,  6480,  6300,  6500,  6160,  6410,  6370, 
6410,  6570,  6480,  6240,  6370,  6430,  6480,  6300,  7400,  7580, 
7620,  7240,  7110,  7220,  7420,  7480,  6390,  6100,  6250,  6250, 
6900,  6270,  6280,  6290,  6270,  6390,  6420,  6120,  6120,  6200, 
6300,  6120,  6430,  6430,  8100,  6100,  6200,  6310,  6204,  6160, 
6170,  6240,  6390,  6140,  6240,  7190,  7240,  7140,  7200,  6340, 
8420,  6310,  7420,  6120  lb.  net.  Find  the  cost  at  $5,871 
per  ton, 

WRITTEN   REVIEW  EXERCISE 

1.  Of  what  number  is  25.56  both  the  divisor  and  quotient? 

2.  The  sum  of  'the  divisor  and  quotient  is  414.06.  If  the 
divisor  is  .6,  what  is  the  dividend? 

3.  In  what  time  will  3  boys  at  $  .75  per  day  earn  as  much 
as  2  men  earn  in  75  da.  at  $2.25  per  day? 

4.  A  merchant  sold  a  quantity  of  flour  for  $370  and  realized 
a  gain  of  $34.  If  the  selling  price  was  $7.40  per  barrel,  what 
was  the  cost  per  barrel  ? 


110  PRACTICAL   BUSINESS   ARITHMETIC 

5.  What  number  is  that  which  is  165  times  as  great  as 
82.5? 

6.  If  450  bbl.   of  beef  sold  for  $5872.50,  what  was   the 
seUing  price  per  hundred  barrels  ? 

7.  What  will  be  the  cost,  at  1 5/  per  yard,  of  a  paper  border 
for  a  room  8  yd.  wide  and  12  yd.  long  ? 

8.  An  article  was  sold  for  S  22.50  ;  if  i  of  the  cost  was  lost, 
what  was  the  loss  ? 

9.  Wood  costing  $3.50  per  cord  is  sold  for  $4.10  per  cord. 
How  many  cords  must  be  handled  to  gain  $240  ? 

10.  Find  the  cost  of  8  bbl.  of  pork  weighing  280,  281,  286, 
290,  285,  277,  285,  and  290  lb.  net,  at  $8.50  per  hundred 
pounds. 

IX.  A  flock  of  200  sheep  was  bought  for  $700.  Ten  of  the 
sheep  died,  and  the  remainder  of  the  flock  was  sold  at  $3.95  per 
head.     What  was  the  gain  or  loss  ? 

12.  If  the  actual  coat  of  the  necessities  of  life  for  one  person, 
in  a  given  year,  amounted  to  $81.45,  and  10  yr.  later,  owing  to 
the  advance  in  prices,  the  same  necessities  cost  $108.60,  what 
was  the  fractional  increase  in  the  cost  of  living  ? 

13.  A,  B,  and  C  bought  a  stock  of  goods  for  $  7500,  A  con- 
tributing $.2500,  B  $3000,  and  C  the  remainder.  They  sold  the 
goods  for  $8400  and  divided  the  profits  equally.  How  much 
of  the  $8400  should  A,  B,  and  C,  respectively,  receive  ? 

14.  The  following  were  the  transactions  of  a  merchant  for 
1  mo.:  merchandise  on  hand  July  1,  $3378.50,  sold  for  cash, 
$2374.20;  boughtfor  cash,  $1945.35;  sold  on  account,  $2276.30; 
bought  on  account,  $876.40  ;  on  hand  July  31,  $2056.35.  Ex- 
penses for  the  month,  $284.25.  What  was  the  net  gain  for 
the  month  ? 

15.  The  following  were  the  transactions  of  a  merchant  for 
1  mo.:  merchandise  on  hand  January  1,  $8120.90;  bought  for 
cash,  $3265.90;  bought  on  account,  $2845.10;  sold  for  cash, 
$5157.65;  sold  on  account,  $4218.25;  on  hand  January  31, 
$7253.25.  The  sale  to  Jas.  S.  Greet,  on  account,  cannot  be 
collected,  $51.20.     What  was  the  net  gam  for  the  month? 


DECIMAL   FRACTIONS  111 

16.  What  is  the  total  freight  on  12,250  lb.  of  hardware  at 
f  .65  per  hundredweight  and  15,670  lb.  of  hardware  at  1.60 
per  hundredweight? 

17.  A  merchant  bought  250  yd.  of  cloth  at  f  3.50  per  yard, 
and  150  yd.  at  ^4.25.  At  what  average  price  per  yard  should 
the  whole  be  sold  to  realize  an  average  profit  of  $1  per  yard? 

18.  What  is  the  cost  of  25  bbl.  of  sugar  containing  312,  304, 
309,  317,  330,  325,  315,  318,  317,  305,  319,  320,  325,  330,  335, 
330,  325,  315,  315,  320,  320,  330,  330,  315,  315  lb.  net,  at  5|^ 
per  pound  ? 

19.  A  received  $1088  from  the  sale  of  his  barley  crop.  If  he 
received  f  0.85  per  bushel  for  the  barley  and  his  farm  produced 
an  average  of  32  bu.  to  the  acre,  how  many  acres  did  it  take 
to  produce  the  barley? 

20.  A  manufacturing  pay  roll  shows  that  40  hands  are  em- 
ployed at  $1.45  per  day,  50  hands  at  S1.40  per  day,  10  hands 
at  13  per  day,  40  hands  at  |2.50  per  day,  and  5  hands  at  18 
per  day.     Find  the  average  daily  wages. 

21.  A  hardware  merchant  found  that  his  stock  of  goods, 
Jan.  1,  amounted  to  134,350.65.  During  the  year  he  bought 
goods  amounting  to  1211,165.45,  and  sold  goods  amounting  to 
1220,540.45.  Dec.  31,  he  took  an  account  of  stock  and  found 
that  the  goods  on  hand  at  cost  prices  were  worth  $81,275.64. 
What  was  his  gain  or  loss  for  the  year? 

22.  Without  copying  the  following  figures,  find  (a)  the  sum 
of  each  line,  and  (6)  the  sum  of  each  column.  Prove  the  work 
by  adding  the  line  totals  and  comparing  the  sum  with  the  sum 
of  the  column  totals. 

17.035  18.0135  186.02  126.42  6.009 

8.005            5.07  142.004  .0634  3.14 

32.972  18.0981  165.42  1.7538  9.314 

126.83              4.931  .628  6.75  .048 

95.16              6.815  .8467  8.41  .062 

101.215  21.214  21.221  2.61  18.641 


112 


PRACTICAL   BUSINESS   ARITHMETIC 


A   REVIEW   TEST 


Without  copying,  find  the  quotients  and  the  sum  of  the  quotients, 
in  each  problem.      Time,  approximately,  forty  minutes. 

In  these  problems  the  quotient  in  each  division  is  apparent  at  a  glance, 
hence  the  attention  is  fixed  on  placing  the  decimal  point. 


1. 

2. 

3. 

12.5- 

-5 

96^.4 

3.9^.3 

1.25- 

-.5 

.96- 

-.004 

39^.03 

.125- 

-.5 

9.6- 

-4 

3.9-^.003 

.125- 

-.05 

.96- 

-.04 

.0039^.003 

.0125-5-5 

9.6- 

-.04 

.039^.0003 

125^.5 

960  ^  .4 

390^.3 

12.5 -^  .05 

.096-^.04 

3.9^3 

.0125^.005 

960^.004 

390-^.03 

12.5^.005 

9.6  ^  .04 

39 -f- .003 

4. 

5. 

6. 

.0065 -f- 1.3 

.69-^23 

.085^.17 

6.5-^1.3 

690-^2.3 

.  .85 -V- .017 

.65-^.13 

6.9  -f-  23 

8.5^.017 

65^.013 

6.9  ^  2.3 

.85^.0017 

6.5^130 

.69^230 

85^.17 

65^130 

.0069^.23 

.085 -f- .0017 

6.5-^1300 

6.9  ^  230 

8.5-^1.7 

.65^13 

.069^.0023 

85 -^  1700 

6500^130 

690^2300 

8.5-^170 

7. 

8. 

9. 

5.7-^.19 

75^.25 

55 -f- 1.1 

57^.019 

75^2.5 

550^1.1 

570^1.9 

.75 -J- 2.5 

.055^110 

57^190 

7.5  -^  250 

5.5-1-110 

.0057^1.9 

.75^.25 

55^110 

5.7^190 

75^.025 

.055-^.011 

57^.19 

.75  ^  250 

550-^.11 

.57^ 

190 

7.5 -i 

-.025 

550^1100 

CHAPTER   XI 

FACTORS,    DIVISORS,    AND    MULTIPLES 

FACTORS 
ORAL  EXERCISE 

1.  Name  two  factors  of  63  ;  of  88  ;  of  144  ;  of  128. 

2.  What  are  the  factors  of  49?  of  77?  of  35?  of  21? 

3.  Name  three  factors  of  45 ;  of  66 ;  of  24 ;  of  60 ;  of  80. 

4.  Name  a  factor  that  is  common  to  35  and  77;  36,  63,  and  81. 

5.  Name  three  factors  that  are  common  to  30,  60,  and  210. 

6.  Which  of  the  following  numbers  have  no  factors  except 
itself  and  one  ?     11,  27,  15,  37,  49,  62,  73,  81,  23. 

141.  An  even  number  is  an  integer  of  which  two  is  a  factor. 
An  odd  number  is  an  integer  of  which  two  is  not  a  factor. 
A  prime  number  is  a  number  that  has  no  integral  factor  except 
itself  and  one.  A  composite  number  is  a  number  that  has  one 
or  more  integral  factors  besides  itself  and  one. 

Numbers  are  mutually  prime  when  they  have  no  common  factor  greater 
than  one. 

WRITTEN  EXERCISE 

1.  Make  a  list  of  all  the  odd  numbers  from  1  to  100  in- 
clusive;  of  all  the  prime  numbers;  of  all  the  even  numbers; 
of  all  the  composite  numbers. 

ORAL  EXERCISE 

1.  Is  2  a  factor  of  28  ?  of  125  ?  of  42  ?  of  49  ?  By  what 
means  do  you  readily  determine  this  ? 

2.  Is  5  a  factor  of  125  ?  of  170  ?  of  224  ?  of  1255  ?  of  1056  ? 
By  what  means  do  you  readily  determine  this  ? 

3.  When  is  a  number  divisible  by  10?  by  3  ?  by  9  ? 

113 


114 


PRACTICAL   BUSINESS   ARITHMETIC 


Tests  of  Divisibility  of  Numbers 

142.    A  number  is  divisible  by : 

1.  Two,  when  it  is  even,  that  is,  when  it  ends  with  0,  2,  4,  6,  or  8. 

2.  Three,  when  the  sum  of  its  digits  is  divisible  by  3. 

3.  Four,  when  the  number  expressed  by  its  two  right-hand  figures  is 
divisible  by  4. 

4.  Five,  when  it  ends  with  0  or  5. 

5.  Six,  when  it  is  even  and  the  sum  of  its  digits  is  divisible  by  3. 

6.  Eight,  when   the    number  expressed   by  the  last   three   right-hand 
figures  is  divisible  by  8. 

7.  Nine,  when  the  sum  of  its  digits  is  divisible  by  9. 

8.  Ten,  when  its  right-hand  figure  is  a  cipher. 

ORAL  EXERCISE 

Name  one  or  more  factors  of  each  of  the  following  numbers: 

1.  184.  5.    6984.  9.    51625.  13.    14128. 

2.  2781.  6.    2750.  10.    83870.  14.    66438. 

3.  1449.  7.    8975.  ii.    13599.  15.    31284. 

4.  638172.  8.    71168.  12.    123125.  16.    17375. 


Factoring 

143.  Factoring  is  the  process  of  separating  a  number  into  its 
factors. 

144.  Example.    Find  the  prime  factors  of  780. 

Solution.  Since  the  number  ends  in  a  cipher,  divide  it  by  the  prime 
factor  6 ;  since  the  resulting  quotient  is  an  even  number,  divide  it  by  2. 
Since  78  is  an  even  number,  divide  it  by  2  ;  since  the  sum  of  the  digits 
in  the  resulting  quotient  is  divisible  by  3,  divide  by  3.  The  prime 
factors  are  then  found  to  be  5,  2,  2,  3,  and  13. 

Id 


5 
2 
2 
3 

780 

156 

78 

39 

WRITTEN  EXERCISE 

Find  the  prime  factors  of: 

1.  112.  4.  786.  7.  968.  lo.  408.  13.  2718.  16.  6900. 

2.  126.   5.  392.  8.  689.  ii.  650.  14.  3240.  17.  2064. 

3.  288.  6.  315.  9.  1098.  12.  762.  15.  3205.  18.  7400. 


EACTOES,   DIVISORS,   AND   MULTIPLES  115 

Cancellation 
oral  exercise 
1.    (4x15) -^(4x3)  =  15  ^3.     Why? 


2.    Divide  2x5x7  by  5x2;  8x7x5  by  5x2x7. 
g    3x7x8^  ^      5x2x8x3^  ^        2x9x7x5 


7x3  2x8x3  5x7x2x3 

4.  What  effect  on  the  quotient  has  rejecting  equal  factors 
in  both  dividend  and  divisor  ? 

145.  Cancellation  is  the  process  of  shortening  computations 
by  rejecting  or  canceling  equal  factors  from  both  dividend  and 
divisor. 

146.  Example.  Divide  the  product  of  6,  8, 12,  32,  and  84  by 
the  product  of  3,  4,  6,  and  24. 

2     2      2      4      28 

^x^x;?[x?i?xfti 


^x^x^x^^ 


2x2  X  2x4x28=  896. 


Solution.  Do  not  form  the  products,  but  indicate  the  multiplication  by 
the  proper  signs  and  write  the  divisor  below  the  dividend  as  shown  above.  3,  4, 
and  6  in  the  divisor  are  factors  of  6,  8,  and  12,  respectively,  in  the  dividend  ; 
hence,  reject  3,  4,  and  0  in  the  divisor  and  write  2,  2,  and  2,  respectively,  in  the 
dividend  ;  then  cancel  the  common  factor  8  from  24  in  the  divisor  and  32  in  the 
dividend,  retaining  the  factors  3  and  4,  respectively  ;  next  cancel  the  common 
factor  3  in  the  divisor  from  84  in  the  dividend  and  there  remains  the  uncanceled 
factors  2,  2,  2,  4,  and  28  in  the  dividend.  Hence,  the  quotient  is  2x2x2x4 
X  28,  or  896. 

WRITTEN  EXERCISE 

1.  14  X  21  X  48  -^  7  X  21  X  6  =  ? 


2.  128  X  48  X  88  ^  64  X  24  X  4  =  ? 

3.  Divide  128  x  18  x  36  by  64  x  18  x  12. 
^  12  X  16  X  24  X  8  x  92  x  28  _  ^ 

6  X  8  X  23  X  7 


116  PRACTICAL   BUSINESS   ARITHMETIC 

5.  If  18  T.  of  hay  cost  1 270,  what  will  25  T.  cost  at  the 
same  rate  ? 

6.  How  many  days'  work  at  12.75  will  pay  for  2  A.  of 
land  at  $110  per  acre? 

7.  If  75  bbl.  of  flour  may  be  made  from  375  bu.  of  wheat, 
how  many  bushels  will  be  required  to  make  120  bbl.  of  flour  ? 

8.  If  45  men  can  complete  a  certain  piece  of  work  in  120 
da.,  how  many  men  can  complete  the  same  piece  of  work  in 
30  da.? 

9.  The  freight  on  350  lb.  of  evaporated  apricots  is  11.47. 
At  that  rate  how  much  freight  should  be  paid  on  7350  lb.  of 
evaporated  apricots? 

10.  If  15  rm.  of  paper  are  required  to  print  400  copies  of 
a  book  of  300  pp.,  how  many  reams  will  be  required  to  print 
32,000  copies  of  a  book  of  300  pp.  ? 

DIVISORS   AND  MULTIPLES 
Common  Divisors 

oral  exercise 

1.  Name  a  factor  that  is  common  to  35  and  49. 

2.  Name  two  factors  that  are  common  to  both  48  and  64. 

3.  Name  the  greatest  factor  that  is  common  to  75  and  100. 

147.  A  common  divisor  is  a  factor  that  is  common  to  two  or 
more  given  numbers.  The  greatest  common  divisor  (g.  c.  d.)  is 
the  greatest  factor  that  is  common  to  two  or  more  given  numbers. 

148.  Example.     Find  the  g.  c.  d.  of  24,  84,  and  252. 

Solutions,     (a)  Separate  each  of  the  num- 
bers into  its  prime  factors.    The  factor  2  occurs  (^) 
twice  in  all  the  numbers  and  the  factor  3  once  24  =2x2x2x3 
in  all  the  numbers.    None  of  the  other  factors  84=2x2x3x7 
occur  in  all  the  numbers;  hence,  2  x  2  x  3,  or  o       o       o       o       7 
12,  is  the  greatest  common  divisor  of  24,  84,  ^'^'^  =^X^XdX'ix7 
and  252. 


FACTORS,   DIVISORS,   AND   MULTIPLES  117 

(&)  The  common  prime  factors  of  two  or  more  given  (5^ 

numbers  may  be  found  by  dividing  the  numbers  by  their  2^)24  —  84  —  25*^ 

prime  factors  successively  until  the  quotients  contain  no  ey^TT^ 7^5 T^TT 

common  factor,  as  shown  in  the  margin.  ^^       ~  '^'^  —  IZo 

^    •     1  r     .•                •  .        -^                 3)6-21-63 
Ever  since  decimal  fractions  came  into  quite  gen-  -^ 

eral  use  the  subject  of  greatest  common  divisor  has  ^         '  "^^ 

been  stripped  of  most  of  its  practical  value.  When  fractions  like  ^||^  were 
quite  generally  used,  it  was  necessary  to  reduce  them  to  their  lowest  terms 
before  they  could  be  conveniently  handled  in  an  operation.  For  this  pur- 
pose, the  greatest  common  divisor  (here  97)  was  found  and  canceled  from 
each  term,  thus  greatly  simplifying  the  fraction  (here  if).  Now,  however, 
the  greatest  common  divisor  of  the  terms  of  the  fractions  used  in  business 
is  easily  found  by  inspection,  and  the  need  for  finding  the  greatest  common 
divisor  is  slight. 

ORAL  EXERCISE 

1.  What  is  the  greatest  common  divisor  of  65  and  75?  of  12 
and  32?  of  75  and  125? 

2.  What  is  the  greatest  common  divisor  of  12,  30,  and  96? 
of  8,  24,  and  42?  of  36,  90,  and  96? 

3.  What  divisor   should   be   used   in   reducing  ^^   to   its 

lowest  teriTm?    12  8?    _6 JL  9    J._6_  ?    _4  8    ?      72   9 
lUWtJbt  teiiiib  .      640-      32  0-      160  *      2i0-      2T0  * 

WRITTEN    EXERCISE 

Find  the  greatest  common  divisor  of: 

1. -48,  240.  2.   42,28,144.  3.   88,144,220. 

4.  A  real  estate  dealer  has  four  plots  of  land  which  he  wishes 
to  divide  into  the  largest  number  of  building  lots  of  the  same 
size.  If  the  plots  contain  168,  280,  182,  and  252  square  rods, 
respectively,  how  many  square  rods  will  there  be  in  each  build- 
ing lot? 

Common  Multiples 

oral  exercise 

1.  Name  a  multiple  of  7 ;  of  9;   of  16;  of  64. 

2.  Name  two  other  multiples  of  each'of  the  above  numbers. 

3.  Name  two  multiples  that  are  common  to  3  and  4  ;  to  5 
and  9 ;  to  8  and  12.  Which  of  the  multiples  just  named  is  the 
least  common  multiple? 


2)14 

21     42 

3)7 

21     21 

7)7 

7       7 

118  PRACTICAL   BUSINESS   AEITHMETIC 

149.  A  common  multiple  is  any  integral  number  of  times  two 
or  more  given  numbers.  The  least  common  multiple  (1.  c.  m.) 
of  two  or  more  numbers  is  the  least  number  which  is  an  integral 
number  of  times  each  of  the  given  numbers. 

150.  Example.     Find  the  1.  c.  m.  of  28,  42,  and  84. 

Solutions,    (a)  Resolve  each  of  the  numbers  into  (^Oi) 

its  prime  factors.  The  factor  2  occurs  twice  in  28  and  9Q__9w9y'7 
in  84,  the  factor  3  occurs  once  in  42  and  84,  the  factor  7  .  ^  ^  „  _ 
occurs  once  in  each  of  the  numbers.  Therefore,  the  'i^  =  ^  X  o  X  i 
least  common  multiple  is  2  x  2  x  3  x  7,  or  84  ;  or  84  =  2  X  2  X  3  X  7 

(&)    Arrange  the  numbers  in  a  horizontal  line  and  divide 
by  any  prime  factor  that  will   exactly  divide  any  two  of  C^) 

them.  Divide  the  numbers  in  the  resulting  quotient  by  any  2)  28  42  84 
prime  factor  that  will  divide  any  two  of  them,  and  so  con- 
tinue the  operation  until  quotients  are  found  that  are  prime 
to  each  other.  Find  the  product  of  the  several  divisors  and 
the  last  quotients  and  the  result  is  the  l.c.m.  2x2x3x7 
=  84,  the  1.  c.  m.  ^ 

All  numbers  that  are  factors  of  other  given  numbers  may 
be   disregarded  in  finding  the  1.  c.  m.       Thus  the   common  multiples  of  4,  8, 
16,  32,  64,  and  80  are  the  same  as  the  multiples  of  64  and  80. 


ORAL  EXERCISE 

State  the  least  common  multiple  of: 

1.  6,  5,  and  3.  4.  2,  4,  7,  8,  48,  24. 

2.  6,  8,  12,  and  24.  5.  6,  42,  84,  168,  336. 

3.  4,  5,  15,  and  30.  6.  5,  15,  75,  150,  300. 

WRITTEN  EXERCISE 
Mnd  the  least  common  multiple  of  : 

1.  6,  7,  8,  and  5.  5.    4,  20,  12,  and  48. 

2.  6,  18,  24,  and  84.  .6.    62,  78,  30,  and  142. 

3.  12,  24,  36,  and  96.  7.    35,  105,  125,  and  225. 

4.  32,  46,  92,  and  128.  8.    114,  240,  72,  and  320. 
9.    What  number  is  that  of  which  2,  3,  5,  and  11  are  the 

only  prime  factors? 


CHAPTER   XII 

COMMON  FRACTIONS 
ORAL  EXERCISE 

1.  When  a  quantity  is  divided  into  3  equal  parts,  what  is 
each  part   called?  into  8  equal  parts?  into  12  equal  parts? 

2.  The  shaded  part  of  A  is  what  part  of  the  whole  liexagon  ? 
the  shaded  part  of  B  ?  the  shaded  part    ^^^      /^W\      A~~A 

3.  In  the   shaded   part  of    A  how    \/  y      \/  v       v  \/ 
many  sixths  ?  in  the  shaded  part  of  B  ? 

4.  One  half  of  the  hexagon  is  how  many  sixths  of  it? 
How  many  sixths  in  the  whole  hexagon? 

5.  In  the  unshaded  part  of  B  how  many  thirds?  Two  thirds 
are  how  many  sixths? 

6.  In  the  unshaded  part  of  C  how  many  sixths? 

7.  Read  the  following  fractions  in  the  order  of  their  size, 
the  largest  first :  i    f ,  f ,  -|,  J,  |,  J. 

8.  Complete  the  following  statement :  Such  parts  of  a  unit 
as  .5,  .25,  J,  |,  etc.,  are  called  . 

151.  Common  fractions  are  expressed  by  two  numbers,  one 
w^ritten  above  and  one  below  a  short  horizontal  line. 

152.  The  number  written  above  the  line  is  called  the 
numerator  of  the  fraction,  and  the  number  written  below, 
tlie  denominator  I  of  the  fraction. 

153.  The  numerator  tells  the  number  of  parts  expressed  by 
the  fraction ;  the  denominator  names  the  parts  expressed  by 
the  fraction. 

Thus,  in  the  fraction  f,  4  tells  that  a  number  has  been  divided  into 
four  equal  parts  and  3  shows  that  three  of  these  parts  have  been   taken. 

119 


120  PRACTICAL   BUSINESS  ARITHMETIC 

154.  It  is  clear  that  the  greater  the  number  of  equal  parts  into 
which  a  unit  is  divided,  the  smaller  is  each  part ;  and  the  fewer 
equal  parts  into  which  a  unit  is  divided,  the  greater  the  size  of 
each  part.    Hence, 

Of  tivo  fractions  having  the  same  denominator^  the  one  having 
the  greater  numerator  expresses  the  greater  value;  and 

Of  two  fractions  having  the  same  numerator^  the  one  having  the 
smaller  denominator  expresses  the  greater  value. 

155.  The  terms  of  a  fraction  are  the  numerator  and  denomi- 
nator. 

156.  A  unit  fraction  is  a  fraction  whose  numerator  is  one. 

Thus  J,  A,  f,  and  J^  are  unit  fractions.     \  in.  is  read  one  third  of  an  inch. 

157.  An  improper  fraction  is  a  fraction  whose  numerator 
is  equal  to  or  greater  than  its  denominator. 

Thus,  f,  f,  and  ^/  are  improper  fractions.  The  value  of  an  improper 
fraction  is  always  equal  to  or  greater  than  one. 

158.  A  mixed  number  is  the  sum  of  a  whole  number  and 
a  fraction. 

Thus,  1\  and  4f,  read  tioo  and  one  seventh  and  four  and  two  ffths,  are 
mixed  numbers. 

ORAL  EXERCISE 

1.  What  takes  the  place  of  the  denominator  in  .5?  in  .25? 

2.  Read  aloud  the  following  fractions  in  the  order  of  their 
size,  the  largest  first  :  -g,  y^,  ^,  3,  3,  iV^  g,  5^,  20'  2  5'  lOO"' 

3.  Read  aloud  the  following  fractions  in  the  order  of  their 
size,  the  smallest  first:  |,  |,  |,  f,  i  |,  J^-,  1,  f,  J,  Jg,  f 

4.  Read  aloud  the  following:  1  mi.;  |T.;  27|-  yd.;  yy^'S' 
cu.  ft.;  275|  A.;  250 jS-  lb.;   <£  IS^^^  ;  <£  2711 ;  -jj^  sq.  ft. 

5.  Of  all  the  cotton  produced  in  the  United  States  in  a  recent 
year  the  principal  cotton-growing  states  contributed  approxi- 
mately as  follows :  North  Carolina,  -^^ ;  South  Carolina,  i ; 
Georgia,  1 ;  Oklahoma  and  Indian  Territory,  -^^ ;  Alabama,  1 ; 
Mississippi,  -^^ ;  Louisiana,  -^-^ ;  Texas,  i ;  Arkansas,  .^V ;  Ten- 
nessee, Jg.  Name  the  principal  cotton-growing  states,  in  the 
order  of  production,  for  that  year. 


HIT 

m  u  M  M 

M  m 

p 

« 

'mA 

mA 

■mmm 

mwimmm. 

COMMON   FRACTIONS  121 

EEDUCTION 
To  Higher  Terms 

ORAL  EXERCISE 

1.  How  many  halves  in  1  ?  how  many  fourths  ?  how  many 
eighths?  how  many  sixteenths? 

2.  How  many  fourths  in  \  ? 
how  many  eighths?  how  many 
sixteenths  ? 

3.  How  many  eighths  in  \  ?  how  many  sixteenths  ? 

4.  How  many  fourths  in  ^|  ?  how  many  eighths  in  1|  ?  how 
many  halves  in  ^^g  ? 

5.  What  effect  is  produced  upon  the  value  of  a  fraction  by 
multiplying  or  dividing  both  terms  of  a  fraction  by  the  same 
number  ? 

6.  Change  14  gal.  to  quarts.  Compare  the  size  of  the  units 
in  14  gal.  with  the  size  of  the  units  in  56  qt.  ;  the  number  of 
units  ;  the  value  of  the  two  numbers. 

7.  Change  1  to  twelfths;   1;   |;   l;   f;   |;   f. 

8.  Name  three  fractions  equal  in  value  to  |^ ;  to  J ;  to  |. 

159.  It  has  been  seen  that  multiplying  or  dividing  both  terms 
of  a  fraction  hy  the  same  number  does  not  change  the  value  of  the 
fraction. 

160.  A  fraction  is  reduced  to  higher  terms  when  the  given 
numerator  and  denominator  are  expressed  in  larger  numbers. 

ORAL   EXERCISE 

1.  Reduce  to  twelfths  :  \,  |,  |. 

2.  Reduce  to  sixteenths :  |,  \,  J,  f . 

3.  Reduce  to  twentieths:  |,  |^,  -f-^,  |,  |. 

4.  Reduce  to  twenty-fourths :  |,  |,  |,  -f^^  f  ^  f  • 

5.  Reduce  to  thirty-seconds :  \,  f ,  f ,  f ,  y^,  yV  W  iV* 

6.  Reduce  to  one-hundredths  :  |,  |-,  -|,  ^,  2T'  A'  i'  /i>* 

7.  Reduce  |  and  |  to  fractions  having  the  denominator  24. 


122  PEACTICAL   BUSINESS  ARITHMETIC 


To  Lowest  Terms 

ORAL  EXERCISE 

1.  2  J  equals  how  many  thirds?  |^  equals  how  many  halves? 

2.  Name  the  largest  possible  unit  frac- 
tion. Why  is  this  the  largest  possible 
unit  fraction  ? 

3.  Change  -f^  to  the  largest  possible 


unit  fraction  ;  y^g  ;  j-^q',  2V0'   iWo^*    Express  ^|  in  its  simplest 
form.     Reduce  2%%  to  its  lowest  terms. 

161.  A  fraction  is  reduced  to  its  lowest  terms  when  the 
numerator  and  denominator  are  changed  to  numbers  that  are 
mutually  prime. 

162.  Example.    Reduce  -^^^  to  its  lowest  terms. 

Solution.     6  is  a  common  factor  of  96  and  108  ;  dividing 
both  terms  by  6,  the  result  is  {|.     2  is  a  common  factor  of        _.0=  1^  =  8. 
16  and  18  ;  dividing  both  terms  by  2,  the  result  is  |. 


ORAL  EXERCISE 

1.  Reduce  to  fifteenths:  J,  -|,  f,  |- 

2.  Reduce  to  eighths  :  2^^,  h  h  Ih  ih  h 

3.  Reduce  to  fiftieths:  1  |,  y2_4_  _.t_^  _8_^  _.u_ 

4.  Change  to  twentieths  :  |,  3^,  f ,  |,  i  -^%,  |. 

5.  Reduce  to  lowest  terms :   ^^g,  -^q.  -f^^  l|,  -^^^  ^. 

WRITTEN  EXERCISE 

1.  Reduce  to  sixteenths  :  llf ,  l|^,  |,  |f ,  |,  iff 

2.  Reduce  to  lowest  terras:  -^^^^  cu.  ft.,  ^4_8_  ^^^   _i4_8_  x. 

3.  Reduce  to  lowest  terms:  lj§  mi.,  Xi-|f,  |ff^  lb.,  |f  mi. 

4.  Reduce  to  three-hundred-twentieths:  -J  mi.,  |  mi.,  ^^   mi. 

5.  Reduce  to  their  simplest  common  fractional  form  :  |^||^  T., 
an  T.,  ^^  A.,  l|i  A.,  11^  sq.  mi.,  Ill  sq.  mi.,  ||f  mi. 


83J. 

4.  666|. 

7.  2655V- 

10.  3150|. 

166|. 

5.  180^. 

8.  319j5j. 

11.  1625J. 

333J. 

6.  212J,. 

9.  14611. 

12.  2150^2 

COMMON   FRACTIONS  123 


Integers  and  Mixed  Numbers  to  Improper  Fractions 

oral  exercise 

1.  How  many  quarts  in  1  gal.?     in  3  gal.? 

2.  How  many  sixths  in  1?     in  3?     in  5?     in  7? 

3.  How  many  fifths  in  1?     in  1|^?     in  1|?     in  3J? 

4.  Express  as  fourths :  6^,  12|,  13,  87,  64,  281. 

5.  Express  as  eighths :  15,  12,  lOJ,  1^,   2f,  If,  ^. 

6.  Express  as  halves :  27,  14,301,^1711    1821    249. 

WRITTEN  EXERCISE 

Reduce  to  improper  fractions : 

1. 
2. 
3. 


Improper  Fractions  to  Integers  or  Mixed  Numbers 

ORAL  exercise 

1.  How  many  pecks  in  240  qt.?    ^|^  =  ?     4"  =  ? 

2.  Change  to  integers:  If^,  1|^  -W,  %»-,  ^^^  ^^K 

3.  Express  28 J  as  fourths ;  express  ^^  as  a  mixed  number. 

4.  Change   to   mixed   numbers:      ^{^,    ij^,   1-f^,    -IfJ^,    ^^. 

5.  What  is  the  value  of :  ^-ff-  lb.?  -\2.8  ib.?  i|  1  bu.?  ^^  pk.? 
W  ft.?  -m'-  A.?  m  mi.?  4<1  lb.?  fll  sq.  ft.? 

written  exercise 
Reduce  to  integers  or  mixed  numbers: 
1     8  5^  rni  4     iJ_2_8.  A  7.    ^#^  lb. 

■■■•      32  0   ^"^*  16  0     -^^  '•         16      ^^' 

2.  -\^3^  A.  5.     IIU  T.  8.     fill  CU.  ft. 

3.  imT.  .        6.    IflfT.  9.    -%Y/sq.mi. 

163.  When  expressing  final  results  reduce  all  proper  frac- 
tions to  their  lowest  terms  and  all  improper  fractions  to 
integers  or  mixed  numbers. 


124  PRACTICAL   BUSINESS   ARITHMETIC 

To  Least  Common  Denominator 

ORAL  EXERCISE 

1.  How  many  pounds  in  1  T.  500  lb.  ?  5  T.  +  1000  lb.  =  ?  lb. 
5  T.  1000  lb.  =  ?  T. 

2.  How  must  numbers  be  expressed  before  they  can  be 
added  or  subtracted? 

3.  1  =  ?  •   1  -L  3  =  ?   1  =  _?L.    1 TL  —  _?_ .   i  —  ? .    1  _  1  _  ? 

''•2        ¥'2^8         "4         16'1         16~16'3~~6'3         6"' 

4.  What  kind  of  fractions  can  be  added  or  subtracted  ? 

5.  Express  |  as  sixteenths.  Add  |  and  -^q  ;  J  and  -^^  ;  | 
and  |. 

6.  Express  ^  as  eighths.  Subtract  J  and  | ;  i  and  -^^  ;  | 
and  Jg. 

164.  Two  or  more  fractions  whose  denominators  are  the  same 
are  said  to  have  a  common  denominator;  if  this  denominator 
is  the  smallest  possible,  the  fractions  are  said  to  have  a  least 
common  denominator.  Two  or  more  fractions  having  the  same 
denominator  are  sometimes  called  similar  fractions. 

ORAL  EXERCISE 
Change  to  similar  fractions : 
1. 
2. 
3. 
4. 

■O'    xv  o 

WRITTEN  EXERCISE 

Change  to  fractions  having  the  least  common  denominator 


hi- 

6. 

4^i- 

11. 

hi- 

16. 

h  h  i- 

ii- 

7. 

hi 

12. 

h^- 

17. 

h  h  h 

hh 

8. 

hi- 

13. 

h  i\- 

18. 

115 

hh 

9. 

hi- 

14. 

h  i\- 

19. 

h  h  1- 

I'A- 

10. 

hi- 

15. 

h  A- 

20. 

h  h  l\ 

1. 

1' 

A'  il 

5. 

6'  1'  t\'   32' 

9. 

iV'  h  f '  A- 

2. 

*' 

iV  A- 

6. 

h    5'  ^6'  A- 

10. 

ih  A'  h  a- 

3. 

i' 

h  1'  4- 

7. 

i'lV'A'H- 

11. 

AV  f '  tVV'  f  • 

4. 

1' 

h  iV  f  • 

8. 

A'  A'  1^2'  h 

12. 

eVo'  tV  A'  A 

Change  the  fractions  to  form  for  addition  or  subtraction : 

13.   31^5,  7t-V        14.   I34J5,  112^.        15.   6126^,178^5. 


COMMOK  FRACTIONS  125 


ADDITION 


165.    It  has  been  seen  that  only  like  numbers  and  parts  of 
like  units  can  he  added. 

ORAL  EXERCISE 

State  the  sum  of: 

1.  |,  |,  f.  7.    21,  3|,  12^,  191. 

2.  i  |,  i.  ■  8.   51,  12^,  7J,  lOJ. 

3.  I,  f,  f  9.    7|,  2|,  81,  IJ,  21. 

*•    A'  fi-  A-  10-    2J,  5f,  8J,  12^,  10|. 

5-  i  i  *,  h  i-  11-    11'  W|,  15J,  18i,  121 

6-  iV'  A-   iV'  !%•  12-    SiV'  2-/j,  IJj,  8^^,  S^lg. 
^^  horizontal  addition  find  the  sum  of: 

13.  2  pieces  of  gingham  containing  41^  and  43^  yd. 

In  the  dry-goods  business  fourths  (quarters)  are  very  common  fractions. 
They  are  usually  written  without  denominators  by  placing  the  numerators 
a  little  above  the  integers.  Thus,  51^  equals  51^,  54^  equals  541  (54^),  and 
528  equals  52f . 

14.  4  pc.  stripe  containing  42^,  38^  40^,  and  49  yd. 

15.  3  pc.  fancy  plaid  containing  42^,  40^,  and  41  yd. 

16.  4  pc.  duck  containing  48^,  47^,  46^,  and  402  j^^ 

17.  2  pc.  monument  cotton  containing  54^  and  b3^  yd. 

18.  4  pc.  dress  silk  containing  32^,  34^,  353,  ^nd  322  y^^ 

166.    Examples,     l.    Find  the  sum  of  ^  and  |. 

Solution.     |  and  |  are  not  similar  fractions  ;  1.  c.  m.  of  8  and  5  =  40 

hence,  make  them  similar  by  reducing  them  to  7  __  3  5.  .    2 IQ. 

equivalent  fractions  having  a  least  common  de-  q  «5  ^  16^^  s  l^  ~-i  1 1 

nominator.      |  =  f^  and  f  =  i§.      fs  +  ^  =  s i  10+10=10  =  ^17 

2.    Find  the  sum  of  56^,  34^,  52f . 

Solution.    By  inspection  determine  the  least  common  561    =    8 

denominator  of  the  given  fractions ;  then  make  the  frac-  o j^  i^    _     o 

tions  similar  and  add  them,  as  shown   in   the   margin.  ^ 

The  result  is  1  ^V,  which  added  to  the  sum  of  the  inte-  1    =  ir. 

gers  equals  143^\,  the  required  result.  -^"^^  A       f  1  =  -^  A* 


126  PRACTICAL   BUSINESS   ARITHMETIC 

WRITTEN   EXERCISE 

Find  the  sum  of: 

1.    ^^,|.  7.    12|,172,V 

3.  21,  17^.  9.  52|,  591,  57|,  52Jg. 

4.  121  19^V  10.  60f,  18f,  21^5_  i42J^. 

5.  1,4^,191.  11.  20^,121,181,921,753. 

6.  21,  4f,  25^%.  12.  140f,  2601,  1451,  216|,  3901. 

13.  A  carpet  dealer  sold  at  different  times  125|  yd.,  272^ 
yd.,  1691  yd.,  186f  yd.,  241i  yd.,  265|  yd.,  296|  yd.,  and 
314|  yd.  of  Axminster  carpet,  at  12.65  per  yard.  If  it  cost 
him  $2.45  per  yard,  what  was  his  gain? 

14.  A  dry-goods  merchant  bought  50  pc.  of  dress  silk  at 
m  per  yard.  If  the  pieces  contained  42^,  43^,  442,  47^,  44^,  452, 
403,  462^  451^  42,  471,  482,  40^,  40i,  402,  40a  592^  493,  472^  433,  403, 
451,  402,  452^  442^  473^  462,  411^  513^  423^  532,  572^  531,  511,  433,  472^ 
401,  452^  452^  403^  401,  453,  472,  481,  511,  522^  572^  613,  602,  50i  yd., 
respectively,  and  he  sold  the  entire  purchase  at  11.25  per  yard, 
what  was  his  gain  ? 

Short  Methods  in  Addition 
oral  exercise 

1.  -I"  +  i  =  Jf •  Observe  that  the  numerator  of  the  sum  is 
equal  to  the  sum  of  the  denominators  in  the  given  fractions. 

2.  -^  + 1^  =  ?  Give  a  short  method  for  adding  any  two  sim- 
ple fractions  whose  numerators  are  1. 

3.  ^  +  I  =  1^1^.  Observe  that  the  numerator  of  the  sum  is 
equal  to  the  sum  of  the  denominators  multiplied  by  the  numera- 
tor of  either  of  the  given  fractions. 

4.  I  4- 1  =  ?  Give  a  short  method  for  adding  any  two  frac- 
tions whose  numerators  are  alike. 

5.  Find  the  sum  of  J,  \,  and  1* 

Solution,     i  4-  i  =  t\  ;  tV  +  3  =  f  ^^  the  required  result. 


COMMON   FRACTIONS 


127 


State  the  sum  of: 


1. 
2. 
3. 
4. 
5. 
6. 

167, 


2'  3 

1  1 

1['  "5 

1  1 

5'  6 

1  1 

y  8 

1  1 

3'  5 


7. 

8. 

9. 
10. 
11. 
12. 


ORAL 

EXERCISE 

h\- 

13.     h  h 

19. 

i  f 

hi- 

14.     |,f 

20. 

f  ^• 

if 

15.     fi 

21. 

h  h  h 

f  *. 

16.     |,f. 

22. 

h  h  h 

f.f 

17.     f,  |. 

23. 

h  h  f 

l-f. 

18.    f  f 

24. 

h  i  I 

The  most  common  business  fractions  are  usually  small 
and  of  such  a  nature  that  they  may  be  added  with  equally  as 
much  ease  as  integers.  The  following  exercise  will  be  found 
helpful  to  the  student  in  learning  to  add  these  fractions  in 
practically  the  same  manner  that  he  adds  integers. 

168.    Example.    Find  the  sum  of  y^g,  |,  |,  and  ^. 

Solution.  By  inspection  determine  that  the  least  common  denominator  is 
16.  Then  mentally  reduce  each  fraction  to  16ths  and  add  as  in  whole  numbers. 
Thus,  5,  7,  19,  H,  m 


OP  AT,  EXERCISE 

Find  the 

«Mm  o/".- 

^ 

1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

9. 

10. 

i 

1 

i 

f 

k 

1 

i 

1 

i 

I 

f 

\ 

i 

i 

1 

1 

i 

t 

i 

i 

i 

1 

1 

1 

1 

3 

1 

1 

1 

J 

2 

6 

6 

10 

3 

^ 

^ 

J 

6 

3 

1 

i 

^ 

i 

i 

i 

1 

i 

ji 

i 

11. 

12. 

13. 

14. 

15. 

16. 

17. 

18. 

.    19. 

20. 

i 

t 

f 

\ 

\ 

I 

J 

i 

* 

1 

2 

1 

t 

1 

f 

6 

i 

1 

i 

1 

i 

i 

1 

1 

f 

f 

1 

f 

i 

1 

2^ 

t 

1 

J 

i 

i 

i 

f 

J 

i 

I 

1 

-,v 

1 

f 

i 

1 

i 

i 

« 

% 

1 

3 

1 

f 

1 

5 

6 

5 

1 

_7_ 

^ 

10 

TJ 

6 

¥ 

? 

6 

^ 

10 

i 

f^ 

A 

1 

1 

A 

1 

\ 

i 

A 

i 

T^ 

A 

i 

f 

iJ 

-h 

I 

i 

i 

Hi 


128  PRACTICAL  BUSINESS  ARITHMETIC 

Exercises  similar  to  the  foregoing  should  be  continued  until  the  student 
can  name  the  successive  results  in  the  addition  without  hesitation. 

169.  The  ordinary  mixed  numbers  that  come  to  an  accountant 
should  be  arranged  for  addition  practically  the  same  as  in- 
tegers. In  adding,  the  fractions  should  be  combined  first  and 
then  the  integers. 

170.  Example.    Find  the  sum  of  2^  5^,  and  3|. 

Solution.  By  inspection  determine  that  the  least  common  denomi-  ni 
nator  of  the  fractions  is  8.  Mentally  find  the  sum  of  the  fractions  and  5 
the  result  is  If.    Add  this  result  to  the  integers  and  the  entire  sum  is  11|.       ^R 

iif 

ORAL  EXERCISE 
State  the  sum  of: 
1.  2.  3.  4.  5.  6.  7.  8.  9.  10. 

2J       3J      Si      8J      iq      5|       4i        2|      31       14i 
3J2|^7|-17|13|-7JWfl7i        16f 

1/    11.       12.  13.         14.        15.        16.        17.        18.        19.         20. 

9|  5|  11  If  8i  4|  5J  41  4^  41 

101  4i  2f  6|  3|  21  2|  5|  2|  If 

13i  IIJ  ^^  51  2J,  4J  41  6f  6t  7| 

lOi  I2J5  8Jj  13|  4J^  3f  6|  2J  3^3^  12J 


21. 

22. 

23. 

24. 

25, 

26. 

27. 

28. 

29. 

30. 

H 

H 

^ 

H 

8i 

4| 

5f 

n 

H 

H 

5i 

^ 

2f 

^ 

6| 

2i 

IJ 

H 

H 

6| 

3| 

5f 

2f 

2f 

H 

H 

91 

7f 

H 

H 

H 

5f 

7f 

6| 

2| 

H 

4* 

5* 

n 

^ 

H 

1| 

1} 

H 

Si 

H 

n 

2f 

n 

8f 

H 

H 

2f 

2f 

5i 

H 

H 

7^ 

H 

2i 

H 

4i 

81V 

3|- 

2i 

H 

2| 

9| 

Hj> 

61 

H 

2t^ 

8^J 

13f 

5A 

H 

12i 

16f 

9t^ 

12i 

Exercises  similar  to  the  above  should  be  continued  until  the  student  can 
add  with  great  facility.  If  the  principles  of  grouping  have  not  been  well 
mastered,  simple  addition  should  be  carefully  reviewed. 


COMMON   FRACTIONS 


129 


WRITTEN  EXERCISE 


Co'py  or  write  from  dictation  and  find  the  sum  of: 


1. 

16491 
43721 
8431| 
51321 
16541 
1831| 
1831| 
14621 
1851^ 


2. 

1672f 
1485| 
16351 
12641 
1269f 
1748J 
1936| 
5413J 
2114,-V 


14361 
1390f 
24151 
18671 
16391 
41361 
16521 
31161 
1439J^ 


4. 

21101 
16401 
36801 
4590J 
2169| 
8432f 
40411 
6542f 
1862| 


1114  j72    1116^6    2243yV   3246 1 


5. 

62141 
1745J 
3146f 
18641 

2839| 
6241| 

4036| 
8130^5_. 

2148^V 
1439^9_ 


6. 

12141 
2167J 
31591 
92751 
7215f 
52611 
7215f 
5144| 
6257| 
2186,-5^ 


7. 

8. 

9. 

10. 

11. 

12. 

91241 

72491 

16491 

75291 

73651 

28141 

27161 
25141 
29671 
29641 
68751 
8875f 
26581 

2724f 
86921 
2476J 
86951 
62141 
72411 
86141 

27241 
8695J 
15651 
2724^ 
86191 
2924| 
65291 

62141 

18251 
86143 
9215f 
6719f 
8516i 
•  7528^ 

26141 
15831 
1695^ 
17621 
1875| 
16291 
7214| 

29101 
2817J 
27141 
2913| 
2874| 
2619f 
14721 

8425| 

4725J 

85921 

7216f 

25101 

2615f 

8273J 

16491 

27251 

67291 

2625f 

18131 

1782f 

12861 

8647| 

35141 

86141 

19621 

8695J 
24721 

6248J 
12861 

8725f 
62191 

1686f 
17251 

2729J 
28161  . 

18621 
17591 

62731 
9685f 
968511 
1925^5_ 

8537f 
69821 
3685J 
26141 

84131 
7226| 
18251 
4725J 

2538f 
1758f 
2752| 
21141 

28141 
2716f 
17621 
18751 

2864| 
16241 
17291 

1805| 

4212^5^ 
2729^2 

87964 
1592| 

2816f 
2519^ 

22161 

18721 

2614| 
2075J 

1721| 
1465f 

130 


PEACTICAL   BUSINESS   ARITHMETIC 


SUBTKACTION 


ORAL  EXERCISE 


t='.^ 


1.  172  A.  -  154  A.  =  ?    f 

2.  Find  the  difference  between  ^ 


1  bu.  -  3  pk.  =  ? 
[ind  ^  ;  J  and  ^;   J  and  |^; 


I  and  |. 

171.  It  is  clear  that  onli/  like  numbers  and  parts  of  like  units 
can  be  subtracted, 

172.  Examples,     i.    Find  the  difference  between  J  and  ■^^. 

Solution.  The  given  fractions  must  be  reduced  to  equivalent  fractions  having 
a  least  common  denominator.  The  least  common  denominator  is  24.  t  =  I?  ^^^ 
h  =  M-     U-H  =  ih  the  required  result. 

2.    From  211  take  17^ 

Solution.  Change  the  given  fractions  to  similar  fractions  as  in  example  1. 
I  cannot  be  subtracted  from  |,  hence  1  is  taken  from  21  and  mentally  united 
to  f,  making  f.  |  from  |  leaves  |,  and  17  from  20  leaves  3.  The  required  result 
is  therefore  3|. 


Find  the  value  of. 

1.  2|-f 

2.  2^-\. 

3.  H-i- 

4.     7|-lf. 


ORAL  EXERCISE 


5. 
6. 
7. 
8. 


H 


45  - 16|. 
11J-6|. 


If.  9.  30-1  If 

6J-4iV  10. 

7^-3^5.  11. 

12|-6|.  12.  70|-20|. 

Tlie  following  is  a  recent  clipping  from  a  daily  paper.  It  shovk^s  the 
prices  of  wheat  on  the  Chicago  market.  The  first  line  of  prices  is  for  wheat 
to  be  delivered  in  July,  and  the  second  line  for  wheat  to  be  delivered  in 
September. 

Chicago  Wheat  Quotations 


Delivery 

Previous  Closing 

Opening 

Highest 

Lowest 

Closing 

July 
September 

87f^ 

87J^ 

92^ 
88J^ 

90f^ 

SI  If 

92-1^ 
87J)^ 

13.  What  was  the  difference  between  the  highest  and  the 
lowest  price  of  July  wheat  ?  of  September  wheat  ? 

14.  What  was  the  difference  between  the  opening  and  the 
closing  price  of  September  wheat?   of  July  wheat? 


COMMON   FRACTIONS  131 

15.  What  was  the  difference  between  the  opening  price  and 
the  previous  closing  (yesterday's  closing)  price  of  July  wheat  ? 
of  September  wheat  ? 

16.  A  bought  1000  bu.  July  wheat  at  the  lowest  price  and 
sold  the  same  at  the  closing  price.     What  was  his  gain  ? 

Suggestion.     lhf  =  $0.015 ;  1000  times  $0,015  =  $ ? 

17.  B  bought  1000  bu.  September  wheat  at  the  opening 
price  and  sold  it  at  the  highest  price.  What  was  his  gain? 
Had  he  bought  at  the  lowest  price  and  sold  at  the  closing  price, 
what  would  have  been  his  gain  ? 

18.  C  bought  25,000  bu.  July  wheat  at  the  opening  price  and 
sold  it  at  the  highest  price.     What  was  his  gain  ? 

WRITTEN   EXERCISE 

5.  1651 -41 3V 

6.  245|-17^3,_. 

7.  177|-17iV 

8.  2150-121i|. 

173.  When  the  numerators  of  any  two  fractions  are  alike,  the 
subtraction  may  be  performed  as  in  the  following  examples. 

174.  Examples.     1.    From  |  take  ^.     2.    From  |  take  |. 

Solutions.  1.  9  —  7  =  2,  the  new  numerator.  9  x  7  =  63,  the  new  denomi- 
nator. Therefore,  the  required  result  is  ^.  2.  8  —  5x3  =  9,  the  new  numer- 
ator.    8  X  5  =  40,  the  new  denominator.     Therefore,  -^^  is  the  required  result. 


Find  the  value 

of 

1. 

39- 

-iii. 

2. 

85- 

-21f. 

3. 

168 

-45f. 

4. 

264- 

1^6-131*. 

9. 

i-l-h 

10. 

l-A-i- 

11. 

2i+lf-l^V 

12. 

25i  -  8f  -  151 

ORAL  EXERCISE 

State  the  value  of 

1-  i-h 

8. 

i-i- 

15. 

I  -  h 

22. 

l-f- 

2-    l-i- 

9. 

i-i- 

16. 

f-f 

23. 

i-i- 

3-    1-^- 

10. 

i-h 

17. 

f-l- 

24. 

f-i- 

*•    i-f 

11. 

l-h 

18. 

l-f 

25. 

i^-^■ 

5-    i-h 

12. 

l-f 

19. 

t-f 

26. 

ni  -  2i. 

6-    i-i- 

13. 

i-h 

20. 

t-f 

27. 

^H-'!h 

'•    i-f 

14. 

k-h 

21. 

§-!• 

28. 

16|  - 12| 

132  PEACTICAL  BUSINESS  ARITHMETIC 


MULTIPLICATION 

ORAL  EXERCISE 

1.  12  times  2  A.  are  how  many  acres?  12  times  2  fifths  (f) 
are  how  many  fifths  ?     -^  =  ? 

2.  32  mi.  divided  by  4  equals  how  many  miles  ?  |  of  32  mi. 
equals  how  many  miles?  Multiplying  by  J,  ^,  ^,  and  1,  etc.,  is 
the  same  as  dividing  by  what  integer  ? 

3.  If  5  men  can  dig  125  bu.  of  potatoes  in  1  da.,  how  many 
bushels  can  3  men  dig  in  the  same  time  ?  |  of  125  bu.  equals 
how  many  bushels  ? 

175.  Example.     Multiply  f  by  248. 

(a) 

Solutions,  (a)  248  times  3  eighths  =  744  eighths  |  X  248  =  ^|^=  93 
=  i|4  =  93;but,  ^ 

(b)  If  the  multiplication  is  indicated  as  in  the  "^I 

margin,  the  work  may  be  shortened  by  cancellation.  f^P  times  o  _  gg 

176.  Therefore,  to  find  the  product  of  an  integer  and  a 
fraction,  find  the  product  of  the  integer  and  the  numerator^  and 
divide  it  hy  the  denominator. 

Before  actually  multiplying,  indicate  the  multiplication  and  cancel  if 
possible. 

ORAL  EXERCISE 

1.  If  1  yd.  of  cloth  costs  i0.87|  (i|),  what  will  16  yd. 
cost?    48  yd.?  128  yd.?  72  yd.? 

2.  When  oats  cost  $0,331  ^(#1)  a  bushel,  how  much  must 
be  paid  for  29  bu.?  for  36  bu.?  for  129  bu.  ? 

3.  A  boy  earns  $0.75  (-f  |)  a  day.  How  much  will  he  earn 
in  18  da.?  in  40  da.?  in  84  da.?  in  128  da.?  in  160  da.? 

4.  When  property  rents  for  $720  a  year,  what  is  the  rent 
for  ^  yr.?  for  \  yr.?  for  \  yr.?  for  ^V  J^'-   ^^r  1  yr.? 

5.  A  ship  is  worth  $48,000.  What  is  \  of  the  ship 
worth  ?  -^^  of  the  ship  ?  f  of  the  ship  ?  |  of  the  ship  ?  {^  of 
the  ship  ? 


COMMON  EKACTIONS  133 

WRITTEN   EXERCISE 

Find  the  product  of : 

1.  98  X  |.  7.  I  of  95.  13.  784  x  f .  19.  f  of  2420. 

2.  80  X  |.  8.  f  of  25.  14.  459  x  f  20.  |  of  2500. 

3.  50  X  2V  9.  I  of  88.  15.  400  X  ^V-  21.  |  of  3240. 

4.  97  X  iV  10-  1^6  of  51.  16.  510  X  iV-  22.  f  of  5117. 

5.  92  X  ^V  11.  -/j  of  99.  17.  990  x  J^.  23.  -/^  of  7254. 

6.  188  Xe^.  12.  iVof77.  18.  800  x  if .  24.  -j^  of  1024. 

177.    Example.     Multiply  25  by  4|. 

25 

Solution.      |  of  25  =  ■?/-  or  9f.     "Write  f  as  shown  in  the  margin, 


and  carry  9  to  the  product  of  the  integers.     4  x  25  +  9  =  109.     There- 
fore, 25  multiplied  by  4|  =  109|.  109| 

178.  Therefore,  to  find  the  product  of  a  mixed  number 
and  a  whole  number,  multiply  the  integer  arid  the  fraction  sepa- 
rately and  find  the  sum  of  the  products, 

ORAL    EXERCISE 

Find  the  cost  of: 

1.  15f  lb.  of  fish  at  9^.  6.  6|  bu.  turnips  at  82^. 

2.  7f  yd.  of  cloth  at  1 3.  7.  12|  bu.  of  oats  at  39^. 

3.  16  lb.  of  beef  at  12|  ^.  8.  l^  yd.  of  calico  at  4^. 

4.  16J  lb.  of  sugar  at  5^.  9.  16J  yd.  of  ribbon  at  20^. 

5.  12  yd.  of  cloth  at  11^^.  10.  8Jgal.  of  molasses  at  40^. 

WRITTEN   EXERCISE 

1.  A  merchant  bought  24  pc.  of  English  serge,  containing  52, 
472,  501,  483,  49,  513,  47,  482,  453,  491,  522,  592,  513,  50,  52,  531, 
523,  473,  481,  512,  513,  482,  49,  and  53  yd.,  at  $1,121-  per  yard,  and 
sold  it  all  at  $1.35  per  yard.     What  did  he  gain  ? 

2.  I  bought  25  pc.  taffeta  silk,  containing  42^,  402,  43,  443, 

45,  412,  43,  401^  472,  44,  452,  491,  471,  451,  46,  44,  433,  40,  41^, 

46,  47,  402,  451,  42,  and  47^  yd.,  at  871/  per  yard,  and  sold 
the  first  15  pc.  at  $1.05  and  the  remainder  at  $1.10.  What 
did  I  gain? 


134 


PRACTICAL  BUSINESS  ARITHMETIC 


3.  A  merchant  bought  25  pc.  of  striped  denim  containing  41^, 
411,  422^  432^  421,  442^  431^  402^  421,  453^  421,  402,  412,  473,  451, 
411,  432^  472^  443^  423^  432^  391,  421,  482^  ^nd  47  yd.,  at  11^  per 
yard.  If  he  sold  the  first  11  pc.  at  15^  per  yard  and  the 
remainder  at  17^  per  yard,  what  was  his  gain? 

4.  Copy  and  find  the  amount  of  the  following  bill: 


^  Little  Falls,  N.Y., 


'^^^-/^  J>^  Y ,       *9 


Terms. 


Bought  of  ^j^^  Eureka  Mills 


di\ 


'^^2^^AP-V-f^.-i?-7:z^ 


^/'  4^^-^  ^j-'  ^^    4^/ ^/^Vvf  J'K^^ 


r  \J2^^  ^:^^^i^^..^^i:'4^'c^^.A^^^^^^. 


^2J  ^/    .^^-^   4^/7-^  A^Z. 


-7^ 


AO_ 


.6U 4^/2- 


y^^. 


179.  The  expressions \^i\ and  \  x  f  have  the  same  meaning  ; 
hence,  the  sign  of  multiplication  may  be  read  0/,  or  multiplied 
hy^  when  it  immediately  follows  a  fraction. 

180.  Examples.     1.    Multiply  |  by  |. 

Solution.     To  multiply  |  by  |  is  to  find  |  of  |. 

Let  the  line  AF  in  the  accompanying  diagram  represent  a  unit  divided  into 
6  equal  parts. 

Then  AD  will  represent  f.     Sub- 
divide each  of  the  five  equal  parts 


M 


M 


M 


into  3  equal  parts  and  the  line  AF 
will  represent  a  unit  divided  into  15 
equal  parts,  each  of.  which  is  -^^  of  the  whole.  It  is  then  clear  that  i  of  \ 
equals  ■^^.  Since  ^  of  ^  is  jV»  i  of  f  is  x\.  But  f  of  f  is  2  times  |  of  f  ;  there- 
fore, I  of  I  equals  ^. 

2.    Find  the  product  of  21  ^,  and  ^. 

Solution.      Reduce  the   mixed   number  2|  to  an  im-  q 

proper  fraction  and  obtain  |.     Cancel,  and  there  remains  in 
the 
which 


per  iraction  ana  ooiam  f .  uancei,  ana  tnere  remams  111  «  ^  ,j  ^  . 
numerators  2  times  7,  and  in  the  denominators  15,  from  ^  ^  ?  ^  TH  =  7^ 
.ch  obtain  the  fraction  f|.  /      ^      15      15 


COMMON  FRACTIONS 


135 


181.    Hence,  to  multiply  a  fraction  by  a  fraction : 

Reduce  the  mixed  numbers  and  integers  to  improper  fractions 

and  cancel  all  factors  common  to  the  numerators  and  denominators. 
Find  the  product  of  the  remaining  numerators  for  the  required 

numerator^  and  the  product  of  the  remaining  denominators  for  the 

required  denominator, 

ORAL  EXERCISE 

1.  How  many  yards  in  |  rd.  ?    feet  in  -|  rd.  ? 

2.  When  barley  is  worth  25|^  per  bushel,  what  is  the  value 
of  ibu.?     of  fbu.? 

3.  A  book,  the  retail  price  of  which  was  $5,  was  sold  at 
wholesale  for  ^  of  the  retail  price,  with  Jq  off  from  that  for 
cash.     Find  the  selling  price  of  10  books. 

WRITTEN   EXERCISE 


5.  50x-^Vx'^l- 

6.  Ifx4ix8|. 


Reduce  to  their  simplest  form  : 

1.  I  of  f  of  f  3.    71  X  25  X  |. 

2.  I  off  of  21  4.    3fx4|x20. 

7.  A  saves  89.75  per  week  and  B  |  as  much.  How  much 
more  will  A  have  than  B  at  the  end  of  a  year  ? 

8.  A  merchant  bought  a  piece  of  cloth  containing  43 1^  yd. 
at  $1.50  per  yard.  He  sold  |  of  it  at  1 1.62 1  a  yard,  and  the  re- 
mainder at  $1.37|  a  yard.     Didhe  gain  or  lose,  and  how  much? 

The  following  is  a  recent  clipping  from  a  daily  paper.  It  shows  the 
prices  of  corn  on  the  New  York  market. 


New  York  Corn  (^ 

;lTOTATIONS 

Dklivkkv 

PKKVIOUS  CU)SIN(} 

Opening 

Highest 

^^OWEST 

Closing 

July 
September 

661/ 
65|/ 

65^/ 
641/ 

661/ 
65|/ 

64|/ 
64^/ 

65|/ 
64f/ 

9.  D  bought  25,000  bu.  September  corn  at  the  opening 
price  and  sold  it  at  the  highest  price.  What  was  his  gain  ? 
Had  he  bought  at  the  lowest  price  and  sold  at  the  highest 
price,  what  would  he  have  gained  ? 


136  PRACTICAL   BUSINESS   ARITHMETIC 

10.  E  bought  12,500  bu.  July  corn  at  the  lowest  price  and 
sold  it  at  the  closing  price.  What  was  his  gain  ?  Had  he 
bought  at  the  lowest  price  and  sold  at  the  highest  price,  what 
would  he  have   gained  ? 

11.  A  gold  dollar  weighs  25.8  troy  grains.  For  every  90 
parts  of  pure  gold  there  are  ten  parts  of  alloy.  How  many 
grains  of  each  kind  in  a  gold  dollar  ?  in  a  5-dollar  gold  piece  ? 

12.  A  5-cent  piece  weighs  77.16  troy  grains.  For  every 
part  of  nickel  there  are  three  parts  of  copper.  How  many 
grains  of  each  kind  in  a  5-cent  piece  ? 

13.  The  second  general  coinage  act  (1834)  of  the  United 
States  made  one  silver  dollar  weigh  approximately  as  much  as 
sixteen  gold  dollars,  and  this  ratio  of  sixteen  to  one  has  been 
maintained  up  to  the  present  time.  What  is  the  approximate 
weight  of  a  silver  dollar  ?  If  silver  coins  are  -^-^  pure,  approxi- 
mately how  much  pure  silver  in  10  silver  dollars? 

Short  Methods  in  Multiplication 

182.  When  mixed  numbers  are  large,  they  may  be  multiplied 
as  shown  in  the  following  example. 

183.  Example.     Multiply  255^  by  24|. 

2551 

Solution.    Multiply  the  fractions  together  242 

and  obtain  ^^,  which  write  as  shown  in  the        ^g   _  2     f  1 

margin.     Multiply  the  integer  in  the  multi-  15       5         3 

plicand  by  the  fraction  in  the  multiplier  and  10  J       =  |  01  ZOO 

obtain  102.    Multiply  the  fraction  in  the  mul-  8       =24  times  J 

tiplicand  by  the  integer  in  the  multiplier  and  ^020 

obtain  8.     Multiply  the  integers  together  and  >^  ^ 

add  the   partial   products.      The   result   is ^ ,  ^  ^ 

6230,v  6230^2^  =24f  times  2551 

WRITTEN  EXERCISE 

Multiply : 

1.  975ibyl8l.  3.    720|by21f.  5.    512^7^  by  161 

2.  876|  by  21  J.  4.    4451  by  46f.  6.   450^9^  by  20|. 


=  24  times  255 


COMMON  FRACTIONS  137 

SQUARING  NUMBERS   ENDING  IN   J   OR  .5 

184.    Examples,     l.    Multiply  9 J  by  Qi. 

Solution.     |  of  I  =  \,  which  write  as  shown  in  the  margin.    ^  9-^ 

of  the  integer  in  the  multiplicand  plus  ^  of  the  integer  in  the  multi-  qj^ 

plier  is  equal  to  either  the  integer  in  the  multiplicand  or  multiplier.  — -| 

Therefore,  add  1  to  the  integer  in  the  multiplicand  and  multiply  by  the  ^^ 
multiplier.     9  x  10  =  90.     Then,  9^  x  9|  =  90^. 

2.  Find  the  cost  of  8.5  T.  of  coal  at  $8.50  per  ton. 

Solution.  The  principles  embodied  in  this  example  are  practi- 
cally the  same  as  those  in  problem  1.  .5  x  .5  =  .25,  8  x  9  =  72. 
Therefore,  8.5  tons  of  coal  at  $8.50  per  ton  will  cost  $72.25.  72.25 

3.  Find  the  cost  of  75  A.  of4a»d  at  $75  per  acre. 

Solution.     This  problem   is  similar  to  example  2,    the  only  75 

difference  being  in  the  matter  of  the   decimal   point.     Since  the  nr 


8.5 
8.5 


5625 


decimal  point  has  no  particular  bearing  upon  the  steps  in  the  pro- 
cess of  multiplying,  proceed  to  find  the  product  as  in  example  2. 
5  X  5  =  25,  which  write  as  shown  in  the  margin.     7  x  8  =  56,  which  write  to  com- 
plete the  product.     75  acres  of  land  at  $75  an  acre  will  therefore  cost  $5625. 


ORAL  EXERCISE 

Multiply : 

1.  11  by  11.  6.  6 J  by  61    11.  131  by  13i.  16.  16i  by  161 

2.  21  by  21  7.  7.5  by  7.5.   12.  141  by  141.  17.  171  by  171. 

3.  31  by  31.  8.  8.5  by  8.5.   13.  151  by  151  18.  ISJ  by  181. 

4.  41  by  41.  9.  9.5  by  9.5.  14.  11.5  by  11.5.  19.  195  by  195. 

5.  51  by  5f  10.  10.5  by  10.5.  15.  12.5  by  12.5.  20.  205  by  205. 

WRITTEN  EXERCISE 

In  the  follotving  problems  make  all  the  extensioiis  mentally. 

1.    Find  the  total  cost  of: 

85  lb.  of  tea  at  85  ^.  b^  lb.  tea  at  bh  ^. 

75  gal.  sirup  at  75^.  75  bbl.  flour  at  17.50. 

45  gal.  sirup  at  45^.  650  bbl.  oatmeal  at  16.50. 

21  bu.  beans  at  $2.50.  25  doz.  cans  olives  at  $2.50. 

35  gal.  molasses  at  35^.  95  cs.  salad  dressing  at  95^. 

^b  cs.  horseradish  at  65^.  750  lb.  cream  codfish  at  71^. 

4^  cs.  baking  powder  at  $4.50.  ^  cs.  baking  powder  at  $3.50. 


138  PRACTICAL  BUSINESS  ARITHMETIC 

MULTIPLICATION   OF   ANY  NUMBERS   ENDING   IN   |    OK    .5 

185.    Examples,     l.    Multiply  TJ  by  GJ. 

Solution,     i  of  the  integer  in  the  multiplicand  plus  |  of  the  integer  g  i 

in  the  multiplier  is  equal  to  i  of  6  +  7,  or  6i,  which  added  to  i  of  ^  rr  j 

equals  6f.     Write  |  as  shown  in  the  margin,  and  carry  6.     6x7  +  6  2 

=  48.    Therefore,  7^  x  6^  =  48|.  48 1 

2.    Multiply  71-  by  OJ. 

71, 

Solution.     |  of  7  +  9  =  8,  with  no  remainder.     1  of  i  =  },  which  ^ 

write  as  shown  in  the  margin,  and  carry  8.      7x9  +  8  =  71.     There-  _^  • 

fore,  7^  X  .91  =  71f.  71 J 

Observe  that  :  (1)  in  finding  ^  of  any  number  (dividing  a  number  by  2) 
there  is  either  nothing  remaining  or  1  remaining;  (2)  in  finding  1  of  an 
even  number  there  can  be  no  remainder,  and  in  finding  ^  of  an  odd  number 
there  is  always  a  remainder  1.  Hence,  to  multiply  numbers  ending  in  i  or  .5 : 
Mentally  determine  the  sum  of  the  integers  in  the  multiplicand  and  multiplier. 
If  it  is  an  even  number,  write  \  (.25  or  25)  in  the  product.  If  it  is  an  odd  num- 
ber,  write  f  (.75  or  75)  in  the  product.  Multiply  the  integers  and  to  the  product 
add  \  of  their  sum. 


Multiply : 

ORAL  EXERCISE 

1.  3^  by  71. 

2.  41  by  51. 

3.  161  by  41. 

4.  171  by  21. 

5.  141  by  61. 

6.  211  by  91. 

7.  3.5  by  8.5. 

8.  7.5  by  6.5. 

9.  5.5  by  8.5. 

WRITTEN   EXERCISE 

Make  the  extensions  in  each  of  the  following  problems  mentally. 

1.  Find  the  total  cost  of  : 

6.5  T.  coal  at  18.50.  8.5  T.  coal  at  $9.50. 

2.5  T.  hay  at  117.50.  16.5  T.  hay  at  111.50. 

15.5  cd.  wood  at  13.50.  14.5  cd.  wood  at  f  5.50. 

2.  Find  the  total  cost  of  : 

45  bu.  beans  at  12.50.  350  bu.  wheat  at  11.05. 

35  bbl.  flour  at  %6.50.  350  bu.  beans  at  12.50. 

45  bbl.  flour  at  $8.50.  85  bbl.  oatmeal  at  $7.50. 


COMMON  FRACTIONS  139 

DIVISION 

ORAL  EXERCISE 

1.  8A.-v-4  =  ?     Snintbs  (|)-^4? 

2.  If  2  lb.  of  coffee  costs  |0.66f  (ff),  what  will  1  lb.  cost? 
Divide  |  by  2.  What  is  the  effect  of  dividing  the  numerator 
of  a  fraction  ? 

3.  4^2  =  ?     J-of.|  =  ? 

4.  Because  |-  -^  2  =  ^  of  |,  therefore,  l  -f-  5  =  i  of  |,  or 
Ivl        ivi— ? 

5.  What  is  the  quotient  of  J  ^  5  ?     of  1^8?     of -1-1-2? 

6.  Because  1^5  =  ^  of  J,  therefore  |  -?-  5  =  2  times  J  of  ^. 
That  is,  I  -^  5  =  1  of  |,  or  I  X  1      f  X  ^  =  ? 

7.  How  much  is  f  ^  5  ?     |  -j-  3  ?     TJ  ( -i/-)  -^  8  ?     31  -  6  ? 

8.  What  is  the  effect  of  multiplying  the  denominator  of  a 
fraction  ? 

186.  In  the  above  exercise  it  is  clear  that 

Dividing  the  numerator  of  a  fraction  hy  an  integer  divides  the 
whole  fraction  ;  and, 

Multiplying  the  denominator  of  a  fraction  hy  an  integer  divides 
the  whole  fraction, 

ORAL  EXERCISE 

Find  the  quotient  of: 

1.  1-4.       4.   1-12.      7.   ^2^4.      10.   f-^9.      13.    1-19. 

2.  38.^2.       5.    1^12.       8.    3-V^9.       11.    1^6,       14.    ^3_^5. 

3.  -U_^5.       6.    fo^3.       9.-^^7.       12.1^5.       15.    ^V- 5. 

187.  Examples.     1.    Divide  28 J  by  7. 

Solution.     First  divide   the  integers  and  the  result  is  4 ;    then  4i 

divide    the    fraction     by     7   and     the    result    is    \.        Therefore, 

28|  ^  7  =  ^. 


7)28J 


2.    Divide  261-  by  8. 


Solution.     Divide  26  by  8  and  the  result  is  3  with  a  remainder  2.  3_5_ 

Join  the  remainder,  2,  vv^ith  the  fraction,  ^,  making  2|.  Reduce  2\ 
to  an  improper  fraction  and  the  result  is  f .  |  -j-  8  =  ^^.  Therefore, 
Sft- 


8)26i 


140 


PRACTICAL   BUSINESS   ARITHMETIC 


Divide : 

ORAL  EXERCISE 

1. 

2. 
3. 
4. 

161  by  4. 
181  by  9. 
25|  by  2. 
171  by  8. 

5.  32|  by  4.    9.  211  by  8. 

6.  271  by  7.   10.  24f  by  6. 

7.  19|  by  9.   11.  45f  by  5. 

8.  20f  by  10.  12.  40f  by  10. 

ORAL  EXERCISE 

13.  81  by  5. 

14.  14|  by  7. 

15.  Ill  by  9. 

16.  26|byl0. 

1.  How  many  eighths  m  one  ?  1  -^- 1  =  ? 

2.  What  is  the  value  of :  1  ^  -^^  ? 

3^1?  17-^1? 

125-^^2?     250-1? 

3.  Read  aloud  the  following,  supplying  the  missing  word : 
To  divide  an  integer  hy  a  unit  fraction^  multiply  the  integer  by 
the of  the  fraction. 

4.  What  is  the  value  of  25  ^  1  ?  2.5 --1?  7.5- |?  25.5^ 
j^?54^i?  48^i?  29-^1?  21^1? 

5.  If  B^  in  the  accompanying  dia- 
gram, is  1,  what  is  (7?  How  many 
blocks  like  C in  Bl   1^^  =  ? 

6.  If  ^  is  1,  what  is  J5  ?  A  is  how 
many  times  B  ?  That  is,  A-i-  B=  ? 
l-f  =  ? 

7.  If  1-^1  =  1  (11),  then  2-f=? 

8.  What  is  the  value  of  4  -  f  ?    5  -  f  ? 

9.  Read  aloud  the  following,  supplying  the  missing  words  : 

If  A  IB,  1^  B  is ,  and  O  is .      If   B  is   contained  in 

A  I  (1|)  times,  it  is  contained  in  (7  1  of  |  times  or times. 

That  is,  l^-5-f 

10. 


12-J-2?   15-1? 


Jx 


What  is  the  value  of  \ 


i? 


2? 
5  • 


1? 
3  • 


3  .^5? 

4  •    6  • 


188.  The  reciprocal  of  a  fraction  is  1  divided  by  that  fraction. 
Thus,  the  reciprocal  of  |  is  1  ->  |,  or  |.    That  is,  the  reciprocal  of  a  fraction 

is  the  fraction  inverted. 

189.  Reciprocal  numbers,  as  we  use  the  terms  in  arithmetic, 
are  numbers  whose  product  is  1. 

Thus,  4  and  \,  |  and  f ,  |  and  6,  f  and  f ,  are  reciprocal  numbers,  because 
their  product  is  equal  to  1. 


COMMON  FRACTIONS 


141 


190.  It  has  been  seen  that  the  brief  method  for  dividing  a 
fraction  or  an  integer  by  a  fraction  is  to  multiply  the  dividend 
hy  the  reciprocal  of  the  divisor. 

The  principles  of  cancellation  should  be  used  whenever  possible.  Inte- 
gers and  mixed  numbers  should  be  reduced  to  improper  fractions  before 
applying  the  rule. 


WRITTEN  EXERCISE 


Divide , 


1. 

2. 
3. 
4. 
5. 
6. 


|byf. 

n  by  h 

95  by  |. 
88  by  f . 


7. 


16  by  f . 
15|  by  1 


10. 

11. 

12. 


fbyf. 

^  by  f . 

fo  by  |. 

^  by  11. 


13-    |byf 


160  by  41 
250  by  3f . 
191.   Examples,     l.    Divide  2190  by  48|. 

Solution.  Multiplying  both  dividend  and  divisor  by 
the  same  number  does  not  affect  the  quotient ;  hence, 
multiply  the  dividend  and  divisor  by  3  and  obtain  for  the 
new  dividend  and  divisor  0570  and  146,  respectively. 
Divide  the  same  as  in  simple  numbers  and  obtain  the 
result  45.     Or, 

Reduce  both  the  dividend  and  divisor  to  thirds,  obtain- 
ing ^-^'^  and  ifs..  Reject  the  common  denominators 
and  divide  as  in  whole  numbers. 

2.    Divide  651  by  12f 

Solution.  Multiply  both  dividend  and  divisor  by  6, 
the  least  common  denominator  of  the  fractions,  and  di- 
vide as  in  simple  numbers.     The  result  is  5f  |.     Or, 

Reduce  both  the  dividend  and  divisor  to  sixths,  obtain- 
ing as  a  result  -'/  and  ^|^.  Reject  the  common  denomi- 
nator and  divide  as  in  simple  numbers. 


14. 


15. 


16. 
17. 
18. 


I  by  f. 
169  by  4|. 
640  by  .5f . 
625  by  83^. 
920f  by  73. 

48|)2190 

_3 3_^ 

146)   6570(45 
584 
730 
730 


121)651 

_6 6_ 

74)  393  (5f  I 
370 
23 


Divide: 

1.  2701  by  121 

2.  508iby30f. 

3.  14311  by  201. 


WRITTEN  EXERCISE 

4.  9621  by  31  J. 

5.  650fby26i. 

6.  1680Jby45i 


7.  7552by78|. 

8.  470fbyl7i. 

9.  10541  by  168f 


142  PRACTICAL   BUSINESS   ARITHMETIC 

FRACTIONAL  RELATIONS 

ORAL  EXERCISE 

1.  If  /  in  the  accompanying  diagram  is 
1,  what  is  el    c??    <??   5?  a? 

2.  What  part  of  e  is/?  of  c??  of  ^?  of 
hi  of  a?  What  part  of  6  is  1?  of  5?  of  4  ? 
of  3?    of  2? 

3.  What  part  of  a  is  6?    dl    cl    hi    What 
•^    "       part  of  6  is  2?    3?    4?    5? 

4.  What  part  of  (^  is/?  What  part  of  5  is  g?  What  part 
of  J  (f )  is  I  ?     What  part  of  f  is  J  (|)  ? 

5.  What  part  of  7  bu.  is  1  bu.?  What  part  of  7  eighths  (|) 
is  1  eighth  (J)  ? 

6.  What  part  of  |  is  |? 

Solution,  f  and  |  are  similar  fractions ;  hence  they  may  be  compared  in 
the  same  manner  as  concrete  integral  numbers.  2  is  §  of  3 ;  therefore,  |  is  |  of 
f;or, 

fis|of|.    |  =  fxf  =  |. 

7.  f  is  what  part  of  1|  (I)?    of  2|?    of  5|?  . 

8.  \  is  what  part  of  J  ? 

Solution.    ^  =  f .     |  is  J  of  f ,  therefore,  l  =  \oi\\  or, 
iisiofi    |=>xf=i. 

192.  To  find  what  fraction  one  number  is  of  another,  take  the 
number  denoting  a  part  for  the  numerator  of  the  fraction^  and  the 
numher  denoting  the  whole  for  the  denominator. 

ORAL  EXERCISE 

1.  If  a  piece  of  work  can  be  performed  in  12  da.,  what 
part  of  it  can  be  performed  in  5  da.  ?  in  7  da.  ? 

2.  If  A  can  do  a  piece  of  work  in  15  da.,  what  part  of  it 
can  he  do  in  1  da.  ?  in  2  da.  ?  in  5  da.  ?  in  1\  da.  ? 

3.  If  B  can  do  a  piece  of  work  in  7 J  da.,  what  part  of  it 
can  he  do  in  1  da.  ?  in  2  da.  ?  in  5  da.  ?  in  SJ  da.  ?  in  ^  da.  ? 


COMMON  FRACTIONS  143 

4.    What  part  of  100  is  331  ?   I2i  ?   66f  ?    8^   25  ?    75  ? 
125?  16f?  831?  621?  22-|  ?  9^^?  56i  ?  6f  ? 

What  part  of  SI  is  331/?  66|/?  25/?  75/?  16f/? 


5.  What  part  ot  ^l  is  55^/  Y   bb|^  Y   :iD^  7   Y£)^  V   ibf  ^ 
81/?  6|/?  31/?  61/?  621/?  871/?  371/?  14|/? 

6.  What  part  of  1000  is  125?  166f  ?  666f  ?  625?  333^  : 

7.  Whatpartof  S10isS3.33i?  S1.25?  S1.66f?  $8.33^ 
S2.50?  S6.25?  S6.66f  ? 


WRITTEN    EXERCISE 

1.  A  man  asked  for  a  horse  |  more  than  it  cost,  but  finally 
reduced  the  price  -^q.  He  gained  $ 26.  What  was  the  cost  of 
the  horse  ?    the  price  asked  ?    the  selling  price  ? 

2.  A  had  1  of  his  money  invested  in  bonds,  -f^  in  bank  stock, 
and  the  remainder,  S1980,  on  deposit  in  the  First  National  Bank. 
How  much  was  invested  in  bonds  ?    in  bank  stock  ? 

3.  A  man  left  his  estate  to  his  four  sons.  To  the  first  son  he 
gave  ^  of  the  estate ;  to  the  second,  i  of  the  remainder ;  to  the 
third,  1  of  the  estate ;  to  the  fourth  son,  $1556.  What  was  the 
value  of  the  estate  ? 

4.  A  merchant  reduced  the  marked  price  of  a  machine  |,  and 
then  sold  it  so  that  he  gained  1  of  the  first  cost.  If  he  gained 
S  8,  what  was  the  first  cost  of  the  machine,  and  the  marked  price 
before  any  reduction  was  made  ? 

5.  A  man  placed  a  house  and  lot  in  the  hands  of  a  real  estate 
agent  to  be  sold  at  such  a  price  that  he,  the  owner,  might  realize 
$5985,  after  paying  the  agent  ^V  ^^  ^^®  selling  price  of  the 
property.     For  how  much  was  the  property  sold  ? 

6.  A  farmer  had  three  bins  containing  wheat,  rye,  and  oats 
respectively.  The  quantity  of  oats  was  three  times  that  of  the 
wheat,  and  the  rye  was  one  half  of  the  quantity  of  the  oats.  If 
the  value  of  the  oats  at  35/  per  bushel  was  $1155,  how  many 
bushels  of  each  kind  of  grain  did  the  farmer  have  ?  If  the 
wheat  was  worth  95/  per  bushel,  and  the  rye  671/  per  bushel, 
what  was  the  value  of  the  entire  lot  of  grain  ? 


144 


PRACTICAL   BUSINESS   ARITHMETIC 


WRITTEN   EXERCISE 

1.  The  square  in  the  margin  represents  the 
total  population  of  the  state  of  New  York  (state 
census  of  1910),  and  the  shaded  area  represents 
the  urban  (city)  population.  If  the  rural  (coun- 
try) population  is  1,800,000,  what  is  the  entire 
population  of  the  state  ?  the  urban  population  ? 

2.  In  a  recent  year  the  population  of  Massachusetts  was  in 
round  numbers  3,360,000,  and  there  were  fourteen  persons  living 
in  the  cities  of  the  state  to  each  person  living  in  the  country. 
Represent  this  graphically  as  in  problem  1,  and  find  the  city 
population  and  the  country  population  for  the  state. 


3.  Suppose  that  Q  in  the  diagram  represents  the  population 
of  the  United  States  in  1870,  A  the  population  in  1830,  and  F 
the  population  in  1900.  If  the  population  in  1870  was  38,400,000 
(round  numbers),  what  was  the  population  (round  numbers) 
in  1900?     In  1830? 

4.  Suppose  that  F  in  the  diagram  represents  the  population 
of  the  United  States  in  1900,  and  O  the  proportion  of  this  popula- 
tion living  in  cities  in  1900.  What  proportion  of  the  popula- 
tion lived  in  cities  in  1900?  Suppose  that  F  represents  the 
population  in  1860  and  A  the  proportion  of  this  population 
living  in  cities.  Assuming  that  the  city  population  in  1860 
was  5,240,554,  find  the  total  population  for  the  same  year. 

5.  The  total  population  of  New  Jersey  (state  census  of  1910) 
is  2,537,167,  and  the  rural  population,  629,957.  Represent  this 
graphically  and  find  the  urban  population, 


COMMON  FRACTIONS  145 


CONVERSION   OF  FRACTIONS 

ORAL  EXERCISE 

1.  What  is  the  denominator  of  the  decimal  .6?  of  .75? 

2.  What  is  the  numerator  of  .4?  of  .04?  of  .004?  of  .0004? 

3.  Write  as  a  common  fraction  .7;  .23;  .079;  .0013;  .00123. 

193.  A  decimal  may  be  written  as  a  common  fraction. 

194.  Examples,     l.    Reduce  .0625  to  a  common  fraction. 

Solution.     .0025  means  yfff^  ;  but  yf  ?^^  may  be  _6.2l_  ^    5_  =,  _1 

expressed  in  simpler  form.    Dividing  both  terms  of  lOOOO       ¥o       iS" 

the  fraction  by  625,  the  result  is  J^. 

WRITTEN  EXERCISE 

Reduce  to  a  common  fraction  or  to  a  mixed  number : 

1.  0.375.  5.   0.9375.  9.   0.0335.  13.  260.675. 

2.  0.0625.         6.   1.66f.  10.   0.0056J.         14.  126.1875. 

3.  0.0016.         7.   0.4375.         ii.   181.875.         15.  175.0625. 

4.  0.5625.         8.   0.125.  12.   171.245.         16.  172.0075. 

195..   A  common  fraction  may  be  written  as  a  decimal. 
196.    Example.    Reduce  |  to  a  decimal. 

Solution,     f  equals  |  of  3  units.     3  units  equals  3000  thou- 
sandths.     \  of  3000  thousands  equals  375  thousandths  (.375).  8)3.000 

ORAL  EXERCISE 

1.  Reduce  to  equivalent  decimals :  J,  \,  |,  J,  |,  J,  |,  |,  |,  |, 
13    5    1   JL   JL  _3_    1    JL 

8'  ¥'  ¥'   8'   16'   12'   16'    9'    11* 

2.  Reduce  to  common  fractions  :  .5,  .25,  .50,  .75,  .33^^,  .QQ^-, 
.16f,  .121  .6,  .4,  .60,  .40,  .2,  .83^,  .20,  .08J,  .375,  .125,  .371 
.87f  .875,  .0625,  .111  .09 Jj. 

WRITTEN  EXERCISE 
Reduce  to  equivalent  decimals : 

1.  |.         3.    Jj.         5.    3f J.       7.    5\V-        9-    It'oo-       "•    21|. 

2.  Jj.       4.    jfg.         6.    if         8.    2V.        10.    5Jj.         12.    1651f 


146  PRACTICAL   BUSINESS   ARITHMETIC 


THE   SOLUTION   OF   PROBLEMS 

197.  The  steps  in  the  solution  of  a  problem  are  :  (1)  reading 
the  problem  to  find  what  is  given  and  what  is  required ;  (2)  de- 
termining from  what  is  given  how  to  find  what  is  required; 

(3)  outlining  a  process  of  computation  and  then  performing  it; 

(4)  checking  results. 

198.  A  problem  should  be  thoroughly  understood  before  any 
attempt  is  made  to  solve  it ;  and  when  the  relation  of  what  is 
given  to  what  is  required  has  been  discovered,  the  process  of 
computation  should  be  briefly  indicated  and  then  performed 
as  briefly  and  rapidly  as  possible. 

199.  To  insure  accuracy  the  work  should  always  be  checked 
in  some  manner.  If  the  answer  to  the  problem  is  estimated  in 
advance,  it  will  prove  an  excellent  check  against  absurd  results. 

Thus,  42  doz.  boys'  hose  at  $48  a  dozen  is  equal  to  approximately 
40  X  1 50 ;  9f  %  of  1290  bu.  is  equal  to  approximately  j\  of  1290  bu.  ;  etc. 

200.  Example.  A  tailor  used  30  yd.  of  flannel  in  making  18 
waistcoats  ;  at  that  rate  how  many  yards  will  he  require  in 
making  45  waistcoats  ? 

Solution 

1.  The  quantity  needed  in  making  18  waistcoats  is  given  and  tlie  quantity 
needed  in  making  45  waistcoats  is  required. 

2.  One  waistcoat  requires  f  ^  yd. ;  45  waistcoats  will  require  45  times  f  §  yd. 
15  5 

3.    — =  75  ;  that  is  75  yd.  of  flannel  are  required  in  making  45 

waistcoats. 

4.  If  yd.  =1  yd.  ;  Jf  yd.  =  f  yd. ;  therefore  the  work  is  probably  correct. 

201 .  If  reasons  for  conclusions,  processes,  and  results  are  given, 
they  should  be  brief  and  accurate.  It  is  also  a  mistake  to  try 
to  use  the  language  of  the  book  or  the  instructor.  Such  artificial 
work  stifles  thought  and  conceals  the  condition  of  the  learner. 

The  subject  of  analysis  should  not  be  unduly  emphasized.  A  correct 
solution  may  generally  be  accepted  as  evidence  that  the  correct  analysis 
has  been  made. 


COMMON   FRACTIONS  147 

ORAL  EXERCISE 

In  the  following  problems  first  find  each  result  as  required,  and  then 
give  a  brief,  accurate  explanation  of  the  steps  taken  in  the  solution.  Do 
not  use  pen  or  pencil. 

1.  If  2  T.  cost  18,  what  will  5  T.  cost? 

Suggestion.  |20;  since  2  T.  cost  |8,  5  T.,  which  are  2^  times  2  T.,  will 
cost2|  times$8,  or  $20. 

2.  24  is  f  of  what  number  ?  f  of  what  number  ?  ^^  of  what 
number  ? 

3.  220  is  ^  less  than  what  number  ?  450  is  I  less  than 
what  number  ? 

4.  A,  having  spent  -J  of  his  money,  finds  he  has  $84  left. 
How  much  had  he  at  first  ? 

5.  1124  is  1  more  than  what  sum  of  money?  fSOO  is  ^ 
more  than  what  sum  of  money? 

6.  A  man  sold  -f^  of  an  acre  of  land  for  $35.  At  that  rate 
what  is  his  entire  farm  of  100  acres  worth  ? 

7.  A  man  bought  a  stock  of  goods  and  sold  it  at  ^ 
above  cost.  If  he  received  $275,  what  was  the  cost  of  the 
goods  ? 

8.  B  bought  a  stock  of  goods  which  he  sold  at  ^  below  cost. 
If  he  received  for  the  sale  of  the  goods  $  240,  what  was  the  cost 
and  what  was  his  loss  ? 

9.  yV  ^^  ^1^®  students  in  a  high  school  are  girls  and  the  re- 
mainder are  boys.  If  the  number  of  boys  is  350,  how  many 
scholars  in  the  school  ? 

10.  A  bought  a  quantity  of  wheat  which  he  sold  at  ^  above 
cost.  If  he  received  $  300  for  the  wheat,  what  did  it  cost  him 
and  what  was  his  gain  ? 

11.  A  bought  a  quantity  of  dry  goods  and  sold  them  so  as  to 
realize  i  more  than  the  cost.  If  the  selling  price  was  $720, 
what  was  the  cost  and  what  was  the  gain  ? 

12.  D  bought  a  stock  of  carpeting  which  he  was  obliged  to 
sell  at  i  below  cost.  If  he  received  $750  for  the  sale  of  the  car- 
peting, what  was  the  cost  of  same,  and  what  was  his  loss  ? 


148  PRACTICAL  BUSINESS  ARITHMETIC 


WRITTEN  EXERCISE 

In  the  following  problems  give  both  analysis  and  computation. 

1.  If  J  lb.  of  tea  cost  21^,  what  will  9^  lb.  cost  ? 

Computation  Analysis 

91  =  J/-  9i  =  Y- ;  9|  is  therefore  19  times  |.     If  |  lb.  cost 

19  X  21  )^  =  $3.99       21  ^,  9|  lb.  will  cost  19  times  21)*,  or  $3.99. 

2.  If  I  of  a  pound  of  tea  cost  42  ^,  what  will  35|  lb.  cost  ? 

3.  If  a  drain  can  be  dug  in  17  da.  by  45  men,  how  many 
men  will  it  take  to  dig  ^  of  it  in  3  da.? 

4.  In  what  time  will  3  boys  at  i0.62|  per  day  earn  as  much 
as  4  men  at  #2.25  each  per  day  will  earn  in  45|  da.  ? 

5.  A  spends  172  per  week  or  |  of  his  income  ;  B  saves 
#48  per  week  or  |  of  his  income.  How  long  will  it  take  A 
to  save  as  much  as  B  saves  in  five  weeks? 

6.  If  115  bu.  of  wheat  are  required  to  make  23  bbl.  of 
flour,  how  many  bushels  will  be  required  to  make  50  bbl.  of 
flour  ?  117  bbl.  of  flour  ?  259  bbl.  of  flour  ? 

ORAL  REVIEW  EXERCISE 

1.  .05x6x0x21=? 

2.  10.75  is  what  part  of  #3? 

3.  What  is  the  sum  of  ^,  |,  ^,  and  -^^  7 

4.  Find  the  value  of  .45-f  (.25  x  5) -.04. 

5.  60  is  I  of  what  number  ?  |  ?  f  ?  f  ?  f  ? 

6.  At  25^  a  yard,  what  will  %  yd.  of  cloth  cost? 

7.  y  is  1^  of  what  number?     |  is  f  of  what  number? 

8.  If  I  of  an  acre  of  land  costs  $75,  what  will  50  A.  cost  ? 

9.  If  I  of  a  number  is  84,  what  is  5  times  the  same  number  ? 

10.  The  dividend  is  4|-  and   the    quotient   is    6|;  what    is 
the  divisor  ? 

11.  If  6  bu.  of  apples  cost  $15,  what  will   80   bu.  cost  at 
the  same  rate  ? 

12.  At    $460    per    half   mile,  what    will    be    the    cost    of 
grading  6  mi.  of  road? 


COMMON  FE ACTIONS  149 

13.  How  much  will  4  carpenters  earn  in  10  da.  at  the 
rate  of  12.25  each  per  day? 

14.  At  $4.50  per  cord,  what  will  be  the  cost  of  4 J  cd. 
of  wood  ?  of  ^  cd.  ?  of  121  cd.  ?  of  7^  cd.  ? 

15.  A  bought  a  horse  for  $96  and  sold  it  for  |  of  its 
cost.     What  part  of  the  cost  was  the  loss  sustained  ? 

16.  A  bought  4J  yd.  of  velvet  at  f  5.20  per  yard  and 
gave  in  payment  a  850  bill.  How  much  change  should  he 
receive  ? 

17.  I  sold  5  A.  of  land  for  $375  and  sustained  a  loss  equal 
to  J  of  the  original  cost  of  the  land.  What  did  the  land  cost 
per  acre  ? 

18.  D  and  E  agree  to  mow  a  field  for  $36.  If  D  can  do 
as  much  in  2  da.  as  E  can  do  in  3,  how  should  the  money 
be  divided  ? 

19.  N  sold  a  watch  to  O  and  received  ^  more  than  it 
cost  him.  If  O  paid  $64  for  the  watch,  what  did  it  cost  N? 
What  per  cent  did  N  gain  ? 

20.  A  earns  $125  per  month.  Of  this  sum  he  spends  $75 
and  saves  the  remainder.  What  part  of  his  monthly  earn- 
ings does  he  save  ?     What  per  cent  ? 

WRITTEN  REVIEW  EXERCISE 

1.  Find  the  cost  of  1100  eggs  at  23|  ^  per  dozen. 

2.  Counting  2000  lb.  to  a  ton,  find  the  cost  of  5J  T.  of 
steel  at  l^g^  per  pound. 

3.  When  flour  is  sold  at  $6.02  per  barrel  of  196  lb.,  what 
should  be  paid  for  55^  lb.  ? 

4.  I  bought  300  bbl.  of  flour  at  $5.75  per  barrel.  At  what 
price  must  I  sell  it  per  barrel  in  order  to  gain  $  150  ? 

5.  The  cost  of  200  bu.  of  wheat  was  $204.50  and  the 
selling  price  $212.35.     What  was  the  gain  per  bushel? 

6.  A  can  do  a  piece  of  work  in  5J  da.  and  B  in  7J  da. 
If  they  join  in  the  completion  of  the  work,  how  long  will  it 
take  them? 


150  .PRACTICAL  BUSINESS  ARITHMETIC 

7.  How  much  will  7  men  earn  in  6  da.,  working  10  hr.  per 
day,  at  25  i  per  hour? 

8.  At  |)2.50  per  day  of  8  hr.,  how  much  should  a  man 
•receive  for  W.\  hours'  work  ? 

9.  A  boy  works  4|^  da.  at  the  rate  of  %bJlb  per  week  of  6 
da.     How  much  does  he  earn  ? 

10.  W,  in  1^  of  a  day,  earns  il.25,  and  Y,  in  |^  of  a  day,  earns 
f  0.87  J.     How  much  will  the  two  together  earn  in  40 J  da.  ? 

11.  A  and  B  together  can  do  a  piece  of  work  in  10  da. 
If  A  can  complete  the  work  alone  in  16  da.,  how  long  will 
it  take  B  to  do  it  ? 

12.  Nov.  1,  in  a  recent  year,  was  on  Tuesday.  How  much  did 
B  earn  during  November  if  he  was  employed  every  working  day 
at  the  rate  of  83.75  per  day? 

13.  A  farm  is  divided  into  6  fields  containing,  respec- 
tively, 25f,  26^7^,  32f,  ^^,  35^9^,  and  52^^  A.  How  much  is 
the  farm  worth  at  837.50  per  acre? 

14.  Find  the  total  cost  of  :  630  lb.  sugar  at  4|^;  375  lb. 
tea  at  38^^;  240  lb.  crackers  at  5|  ^  ;  ^b  lb.  rice  at  7y9g  ^ ; 
521  lb.  raisins  at  7i-^;  and  250  lb.  coffee  at  24f  ^. 

15.  A  retailer  bought  5  bbl.  of  flour  at  86.50  per  barrel, 
12  bu.  potatoes  at  75  ^  per  bushel,  and  gave  in  payment  a 
fifty-dollar  bill.     How  much  change  should  he  receive  ? 

16.  Five  garden  lots  measuring  2|^,  lOJ,  12|,  6y^,  and 
8j9g  A.  respectively,  were  bought  at  8212.87|^  per  acre  and 
sold  at  8250.50  per  acre.  Find  the  gain  resulting  from  the 
transaction. 

17.  I  bought  4120  2  yd.  of  silk  at  81.02  per  yard  and  sold 
\  of  it  at  81.50  per  yard,  and  the  remainder  for  81600. 
What  was  the  average  price  received  per  yard,  and  how 
much  did  I  gain? 

18.  A,  B,  C,  and  D  hire  a  pasture  for  8419.50.  A  put  in 
25  head  of  cattle  for  4  wk.;  B,  31  head  for  5  wk.;  C,  44 
head  for  6  wk.;  and  D,  40  head  for  8  wk.  How  much 
should  each  be  required  to  pay  ? 


COMMON   FRACTIONS  151 

19.  A  grain  dealer  bought  6750 J  bii.  of  corn  at  60 J  ^  per 
bushel,  and  2130J  bu.  of  oats  at  32|  ^  per  bushel.  He  sold 
the  corn  at  69|  ^  per  bushel,  and  the  oats  at  39|  ^  per  bushel. 
Did  he  gain  or  lose,  and  how  much  ? 

20.  A  grocer  bought  15  bbl.  of  molasses,  each  containing 
50  gal.,  at  25^^  per  gallon.  He  retailed  150^  gal.  of  it  at 
30^  per  gallon,  170i  gal.  at  28^  per  gallon,  and  the  re- 
mainder at  35^  per  gallon.  Did  he  gain  or  lose,  and  how 
much  ? 

21.  Find  the  cost  of  25  bx.  of  cheese  weighing :  67  —  4, 
62-4,  61-3,  72-4,  81-5,  64-4,  66-3,  65-5,  61-4, 
62-3,  64-4,  66-3,  65-5,  61-4,  62-3,  64-4,  67-3, 
65-5,  60-3,  62-4,  67-4,  65-4,  60-4,  68-3,  65-4 
lb.,  respectively,  at  11 1  ^  per  pound. 

22.  A  dry-goods  merchant  bought  25  pc.  of  Scotch 
cheviot  containing  42^,  402,  453^  411^  401,  452^  421,  43^,  38^, 
351,  302,  412^  441^  452^  391^  371^  422^  47,  41,  42^,  43^,  40^,  47^, 
38,  31  yd.,  respectively,  at  39^^  per  yard.  If  he  sold  the 
entire  purchase  at  43|^  per  yard,  did  he  gain  or  lose,  and 
how  much  ? 

23.  C.  W.  Bender  failed  in  business.  He  owes  A  $712.25; 
B,  11421.25;  C,  1625.25;  D,  $1460.75;  his  entire  resources 
amount  to  $2109.75.  What  fractional  part  of  his  indebted- 
ness can  he  pay?  what  per  cent?  How  many  cents  on  f  1  ? 
If  his  creditors  accept  payment  on  this  basis,  how  much  will 
each  receive  ? 

24.  A  dry-goods  merchant  bought  12  pc.  of  striped 
denim  containing  40^,  45i,  40^,  482,  412,  403^  452^  4II,  442, 
392,  511,  33  j^^^  respectively,  at  14|^  per  yard;  15  pieces  of 
cashmere  containing  39^,  412,  421,  452^  39,  52,  40,  45,  46,  51, 
472,  421,  411,  471^  48  yd.,  respectively,  at  $1.12  per  yard;  10 
pc.  wash  silk  containing  35 1,  30,  312,  30^  30,  30,  32^,  32,  31 1, 
32  yd.,  respectively,  at  31^  per  yard.  He  gave  in  payment, 
cash,  $300,  and  a  60-da.  note  for  the  balance.  What  was  the 
face  of  the  note  ? 


152 


PRACTICAL  BUSINESS  ARITHMETIC 


25.   Find  the  amount  of  the  following  bill : 

Boston,  Mass.,  Apr.  15,  19 

Messrs.  Charles  H.  Palmer  &  Co. 

Springfield,  Mass. 

Bought  of  Edgar  W.  Townsend  &  Co. 

Terms:  cash 


250 

lb.  Rio  Coffee 

$0.24| 

450 

"   Mocha  Coffee 

.20i 

172 

doz.  Eggs 

.241 

990 

lb.  White  Sugar 

.041 

900 

"   Brown  Sugar 

.031 

975 

"  Granulated  Sugar 

.041 

172 

"   Butter 

.161 

3021 

"   Ham 

.\^ 

280 

"   Cream  Codfish 

.071 

11 

pails  Mackerel 

1.87| 

120 

lb.  Raisins 

•07f 

480 

"   Starch 

.03| 

225 

"  Japan  Tea 

.26^ 

210 

"  Young  Hyson  Tea 

.241 

420 

"   Oolong  Tea 

.271 

157 

"   Pearl  Tapioca 

•03| 

17 

pkg.  Yeast  Cakes 

.37^ 

375 

lb.  Java  Coffee 

•231 

26.  C's  salary  is  $17.50  per  week  of  48  hr.  How  much 
should  he  be  paid  for  11  da.,  working  9  hr.  per  day? 

27.  A  man  earning  |2.75  per  day  of  10  hr.  lost  7 J  hr. 
during  one  week  of  6  da.  How  much  should  he  receive  for 
the  week's  work  ? 

28.  E  begins  work  at  7:30  A.M.  and  quits  work  at  6:30  p.m. 
If  he  is  paid  at  the  rate  of  $3.75  per  day  of  8  hr.  and  he  takes 
the  noon  hour  off  for  lunch,  how  much  should  he  receive  for 
his  day's  labor  ? 

29.  A  factory  foreman  is  paid  $3.75  per  day  of  8  hr.  and 
$0.50  an  hour  for  overtime.  How  much  should  he  be  paid  for 
a  week  in  which  he  begins  work  at  7  o'clock  A.M.,  quits  work  at 
7:30  o'clock  p.m.,  and  takes  1\  hr.  off  each  day  for  lunch? 


COMMON   FKACTIOISrS 


153 


GEAPHIC   OUTLINE 

A  comparison  of  the  money  value  of  the  wheat  crop,  and  the  fire  losses 
paid  by  insurance  companies,  in  the  United  States,  1890  to  1899  inclusive. 
value  of  wheat  crop.    value  of  fire  losses. 


1890 

1891 

1892 

1893 

1894 

1895 

1896 

1897 

1898 

1899 

800  million  dollars 

700  million  dollars 

GOO  million  dollars 

500  million  dollars 

A 

400  million  dollars 

/\ 

A, 

300  million  dollars 

/ 

t 

\ 

\ 
\ 

\ 

i 

. / 

/      ^s 

\ 

200  million  dollars 

v 
\ 
\ 

___^„ 

100  million  dollars 

1 

'' 

1 

WRITTEN    EXERCISE 

1.  The  figures  below  give  the  value  of  the  wheat  crop,  and  the 
fire  losses  paid  by  fire  insurance  companies,  in  the  United  States, 
for  the  years  1890  to  1899  inclusive.   (See  Graphic  Outluie.) 

Farm  Val.  of  Wheat  Fire  Losses 

1890  8334,773,678  S108,993,792 

1891  513,473,711  143,764,967 

1892  322,111,881  151,516,098 

1893  213,171,381  167,544,370 

1894  225,902,025  140,006,484 

1895  237,938,998  142,110,233 

1896  310,602,593  118,737,420 

1897  428,547,121  116,254,575 

1898  392,770,320  130,593,505 

1899  319,545,259  153,597,830 


164  PRACTICAL   BUSINESS   ARITHMETIC 

2.  Make  a  graphic  outline  comparing  the  wheat  crop,  and  the 
fire  losses  paid  by  the  fire  insurance  companies,  in  the  United 
States,  for  the  years  1880  to  1889  inclusive. 


Farm  Val.  of  Wheat 

Fire  Losses 

1880 

$474,201,850 

$74,643,400 

1881 

456,880,427 

81,280,900 

1882 

445,602,123 

84,505,024 

1883 

383,649,272 

100,149,228 

1884 

330,862,260 

110,008,611 

1885 

275,320,390 

102,813,796 

1886 

314,226,020 

104,924,750 

1887 

310,612,960 

120,283,055 

1888 

385,248,030 

110,885,665 

1889 

342,491,707 

123,046,833 

3.  Make  a  graphic  outline  comparing  the  wheat  crop,  the  cotton 
crop,  and  the  fire  losses  paid  by  the  fire  insurance  companies,  in 
the  United  States,  for  the  years  1900  to  1909  inclusive. 


Farm  Val.  of  Wheat 

Farm  Val.  of  Cotton 

Fire  Losses 

1900 

$323,515,177 

$515,828,431 

$160,929,805 

1901 

467,350,156 

439,166,710 

165,817,810 

1902 

422,224,117 

501,897,135 

161,087,040 

1903 

443,024,826 

660,549,230 

145,302,155 

1904 

510,489,874 

652,031,626 

229,198,050 

1905 

518,372,727 

632,298,332 

165,221,650 

1906 

490,332,760 

721,647,237 

518,611,800 

1907 

554,437,000 

700,956,011 

215,084,709 

1908 

616,826,000 

681,230,956 

217,885,850 

1909 

730,046,000 

812,089,833 

188,705,150 

Use  a  dotted  line  to  represent  the  cotton  crop. 

The  figures  representing  the  fire  losses  do  not  include  the  cost  of  main- 
taining fire  departments,  nor  the  losses  sustained  by  the  interruption  of 
business. 

The  United  States  exceeds  all  other  countries  in  losses  by  fire.  A  large 
per  cent  of  these  losses  are  due  to  carelessness. 


COMMON   FRACTIONS  155 


ORAL    REVIEW   EXERCISE 


1.  I  of  36  is  what  part  of  81  ? 

2.  Multiply  126  by  101;  92  by  102. 

3.  Divide  41  by  2| ;  3f  by  21. 

4.  Find  the  cost  of  each  of  the  following : 

a.    35  bn.  of  seed  at  35/  per  bushel. 
h.    65  A.  of  land  at  $65  per  acre. 
c.    45  yd.*  of  cloth  at  45/  per  yard. 

5.  Divide!  by -I;  %^y  ^^  t  by  f 

6.  Multiply  86  by  f  ;  49  by  f  ;  55  by  -j^. 

7.  What  is  the  square  of  15  ?  of  1.5  ?  of  IJ  ? 

8.  64x1  =  ?  64^i  =  ?  1  +  1  +  1=? 

9.  How  many  yards  of  cloth  can  be  bought  for  S25  at  121/ 
per  yard  ? 

10.  If  it  costs  $7.50  to  harvest  61  A.  of  corn,  what  will  it 
cost  to  harvest  65  A.  ? 

11.  An  agent  received  $7.20  for  collecting  a  debt,  and  the 
merchant  received  $232.80.     What  was  the  total  debt? 

12.  C  and  D  received  $  21.75  for  work  done  jointly.  If  C  does 
only  half  as  much  work  as  D,  how  should  the  money  be  divided  ? 

13.  If  a  lot  of  articles  were  bought  at  the  rate  of  3  for  2/  and 
sold  at  the  rate  of  2  for  3  /,  how  many  must  be  sold  to  gain  $  5  ? 

14.  A  and  B  received  $  34  for  work  done  jointly.  If  A  can 
do  as  much  work  in  8  da.  as  B  can  do  in  9  da.,  how  should  the 
money  be  divided  ? 

15.  Name  the  results  quickly : 

a.  A  can  do  a  piece  of  work  in  4  da.,  and  B  in  5  da.  If  they 
work  together,  in  how  many  days  will  they  finish  the  task  ? 

h.  F  can  do  a  piece  of  work  in  31  da.,  and  G  in  5  da.  If  they 
work  together,  in  how  many  days  will  they  finish  the  task  ? 

c.  C  can  do  a  piece  of  work  in  2  da.,  D  in  3  da.,  and  E  in  4  da. 
If  they  work  together,  in  how  many  days  will  they  finish  the  task  ? 

d.  H  and  J  together  can  do  a  piece  of  work  in  20  da.  If  H 
alone  can  do  the  work  in  30  da.,  in  how  many  days  can  J  alone 
do  the  work  ? 


156  PRACTICAL   BUSINESS   ARITHMETIC 

written  exercise 
Problems  of  the  Farm 

1.  If  15  sheep  consume  5785  lb.  of  dry  fodder  in  a  year,  what 
is  the  cost  per  sheep  if  the  fodder  is  worth  S8.50  per  ton  ? 

2.  If  eggs  are  worth  24^  per  dozen,  what  is  the  difference 
in  the  value  of  two  hens,  in  a  year,  if  one  lays  180  eggs  and  the 
other  lays  96  eggs  ? 

3.  An  apple  tree  produced  9^  bu.  of  apples,  6  J  bu.  of  which 
graded  as  "  firsts  "  and  the  remainder  as  "  seconds."  What  frac- 
tional part  of  the  yield  were  firsts,  and  what  fractional  part  were 
seconds  ? 

4.  The  apple  tree  referred  to  in  Ex.  3  was  sprayed  the  year 
following,  and  that  year  it  produced  10^  bu.  of  which  9^  bu. 
were  firsts  and  the  remainder  seconds.  What  fractional  part  of 
the  yield  were  firsts  ?    What  part  were  seconds  ? 

5.  If  the  apples  referred  to  in  Exs.  3  and  4  were  sold  at  S1.20 
per  bushel  for  firsts  and  70  /  sl  bushel  for  seconds,  what  was  the 
value  of  the  spraying  ? 

6.  It  is  estimated  that  a  quail  in  one  year  eats  28/  worth 
of  grain  and  saves  S1.68  worth  of  grain  by  destroying  insects 
and  weeds.  What  is  the  value  of  a  pair  of  quails  to  the  farmer 
annually,  not  counting  the  value  of  the  brood  ? 

7.  An  undrained  field  produced  24  bu.  of  grain  per  acre,  and 
after  being  drained  it  produced  33  bu.  per  acre.  What  was  the 
fractional  increase  ?  What  was  the  value  of  the  increase  if  the 
grain  sold  for  55^^/  per  bushel  ? 

8.  A  flock  of  hens  averaged  78  eggs  each  per  year.  What 
would  be  the  value  to  the  farmer  of  introducing  a  better  breed 
of  hens  that  would  produce  120  eggs  each  per  year,  if  he  kept 
a  flock  of  40  hens,  and  received  24/  per  dozen  for  the  eggs  ? 

9.  If  6  A.  of  unfertilized  land  produced  275  bu.  of  corn,  and 
if  fertilized,  it  would  have  produced  350  bu.,  what  would  the 
farmer  have  gained  by  fertilizing  the  land  if  the  corn  was  sold 
for  68  /  per  bushel,  and  the  fertilizer  cost  $  24  per  ton,  and  400  lb. 
were  used  on  each  acre  ? 


COMMON   FRACTIONS  157 

WRITTEN  REVIEW  TEST 
(Time,  approximately,  forty  minutes) 

1.  A,  B,  and  C  hire  a  pasture  for  $81.  A  puts  in  6  cows  for 
4  mo. ;  B,  6  cows  for  6  mo. ;  and  C,  6  cows  for  5  mo.  What  sum 
should  each  pay  ? 

2.  A  man  owned  |^  of  a  tract  of  land ;  he  sold  |  of  his  share 
for  $14,504.46.  At  that  rate,  what  was  the  value  of  his  original 
share  ?    What  was  the  whole  tract  worth  ? 

3.  The  owner  of  a  house  received  a  net  yearly  income  from 
rental  of  $408.90,  after  paying  the  following  :  insurance,  $64.20  ; 
taxes,  $74.50  ;  repairs,  $28.40.    What  was  the  monthly  rental? 

4.  A  man  drew  i  of  his  money  from  the  bank  and  then  paid 
bills  of  the  following  amounts:  $12.50,  $18.25,  and  $7.50;  he 
then  had  left  in  cash  $11.75.  What  sum  had  he  in  the  bank 
before  drawing  the  check  ? 

5.  A  man  placed  a  mortgage  on  his  house  and  lot  for  $2967. 
The  lot  cost  $2720  ;  the  improvements,  $260.50;  and  the  dwell- 
ing, $5920.50.  The  mortgage  was  what  fractional  part  of  the 
total  value  of  the  property  ? 

6.  At  the  end  of  a  season  a  dealer  sold  a  machine  for  $64, 
after  reducing  the  marked  price  ^.  If  he  still  gained  ^  of  the 
cost,  what  was  the  first  cost?  The  marked  price  was  what 
fraction  above  the  cost  price  ? 

7.  From  dictation,  write  results  for  the  following:  |  of 
25J;  J  of  26i;  1  of  36^;  |  of  17i;  J  of  42|;  1  of  281;  J_  of 
22J ;  1  of  641  ;  i  of  50  \;  ^\  of  35^ ;  J^  of  501. 

8.  A  merchant  closed  his  business  under  the  following  con- 
ditions:  resources,  $22,455.20;  liabilities,  $33,682.80.  What 
fractional  part  of  his  debts  can  he  pay  ?  If  he  owes  James  S. 
Brown  $202.50,  how  much  will  Brown  receive  in  settlement? 

9.  A,  B,  and  C  are  partners  in  a  mercantile  business  in 
which  A  has  invested  $9180  ;  B,  $6120  ;  and  C,  $3060.  At  the 
end  of  1  yr.  they  divided  a  gain  of  $3060.90.  If  each  partner 
received  of  the  gain  according  to  his  fractional  part  of  the 
investment,  how  much  did  each  receive? 


CHAPTER  XIII 

ALIQUOT   PARTS 

202.    An   aliquot  part  of  a  number  is   a  part  that  is  con- 
tained in  the  number  an  integral  number  of  times. 
Thus,  2^,  3|,  and  5  are  aliquot  parts  of  10. 

ORAL  EXERCISE 

1.  How  many  cents  in  |i?  in  |l?  in  Si?  in  $1? 

2.  What  aliquot  part  6f  |1  is  25^?  50^?  6|^?  12^? 

3.  Read  aloud  the  following,  supplying  the  missing  terms : 
16  X  50^  =  16  X  1 1  =  1  of  116 ;  16  x  25^  =  16  x  I J  =  ^  of  116 ; 

16xl2i^=16xf = of  816;  16x6^^=16x1 

= of  $16. 

4.  Give  a  short  method  for  finding  the  cost  when  the  quan- 
tity is  given  and  the  price  is  50^;  25^;   12-|^;  6J^. 

5.  What  is  the  cost  of  160  yd.  of  dress  goods  at  |1?  at  50^? 
at  25^?  at  121^2^?  at  6J^? 

6.  How  many  cents  in  |i?  in  IJ?  in  $^j?  in  |  Jg?  in  |^? 
in$^?inl3-V? 

7.  What  aliquot  part  of  II  is  33i^?    16|^?    SJ^?    6|^? 
14f^?  20^?  lOi^? 

8.  Read  aloud  the  following,  supplying  the  missing  terms  : 

140xl4f^  =  140  X  $i  =  |  of  $140;  90  x  6f^  =  90  x  $ 

= of  190;  90x20^  =  90x$ = of  $90. 

9.  Read  aloud  the  following,  supplying  the  missing  terms : 

240x331^=240x1 =|    of    $240:    240xl6f  =  240x 

$1  = of  $  240;   240  x  12^^  =  240  x  $ = of  $  240. 

10.  Give  a  short  method  for  finding  the  cost  when  the  quan- 
tity is  given  and  the  price  is  331^;    16|^;   8J^;   6|^;   14f^. 

11.  Find  thecost  of  960  yd.  of  cloth  at  331^;  at  16f  ^;  at  Sy. 

158 


ALIQUOT   PARTS  159 

ORAL  EXERCISE 

State  the  cost  of: 

1.  240  lb.  tea  at  bO^;  "at  33J^;  at  25^. 

2.  3601b.  cofPee  at  331^;  at  25^;  at  20^;  at  121^. 

3.  720  gal.  cider  at  6^^;  at  6|^;  at  10^';  at  12 J^. 

4.  2400  doz.  eggs  at  121^;  at  lOf^;  at  20^;  at  25^. 

5.  2400  yd.  prints  at  8J^;  at  6|^  ;  at  6J^;  at  12^1^. 

6.  960  yd.  cotton  at  6i^;  atSl^;  at6f^;   at  10^;   at  12^^. 

7.  2040  yd.  plaids  at  50^;  at  331^;  at  25^ ;  at  20^;  at  16f  ^. 

8.  480  1b.  lard  at  81^;  at  6^^;  atl2i^;  at  16|^;  at  10^. 

9.  36001b.  raisins  at  121)!^;  atl6|^;  at20^;at25^;  at  331^. 

10.  480  yd.  lining  at  81^;   at6|^;  at  10^;  atl2i^;  at6|^. 

11.  4200  yd.  Silesia  at  10^;  at  20^;  at  12^^;  atl6f^;  at  142^. 

12.  1500  yd.  plaids  at  81;  at  50^;  at  33^]^;  at  25  ^ ;  at  20  ^. 

13.  420  yd.  stripe  at  10^;  at  12^^;  at  14|^;  at  16f  ^;  at  25^. 

14.  120  yd.  gingham  at  81^;  at  6^^;  at6f^;  at  loV;  at  121^. 

15.  1240  yd.  wash  silk  at  25^;  at  50^;  at  33^^;  at  20^. 

16.  At  the  rate  of  3  for  50^,  what   will  27  handkerchiefs 
cost? 

17.  At  331^  per  half  dozen,  what  will  12  doz.  handkerchiefs 
cost?  17  doz.?  25  doz.?  7 J  doz.?  41  doz.? 

18.  A  merchant  bought  cloth  at  33 J  ^  per  yard  and  sold  it 
at  50^  per  yard.     What  was  his  gain  on  1680  yd.? 

ORAL  EXERCISE 

1.  What  is  the  cost  of  12^  yd.  of  silk  at  96  ^  per  yard? 
Suggestion.     The  cost  of  12i  yd.  at  96^  =  the  cost  of  96  yd.  at  12^  ^ 

Interchanging  the  multiplicand  and  multiplier  considered  as  abstract  numbers 
does  not  affect  the  product. 

2.  Find  the  cost  of  25  yd.  of  silk  at  11.72  per  yard. 
Suggestion.    The  cost  of  25  yd.  at$  1.72  (172 j>)  =  the  cost  of  172  yd.  at  25^. 

3.  Find  the  cost  of : 

a.  25  yd.  at  16^.       c.    6|  lb.  at  32^.       e.    25  yd.  at  84^. 

b.  121yd.  at  48^.     d.    12^  lb.  at  80^.     /.    12iyd.  at  |1.75. 


160  PEACTICAL  BUSINESS  AEITHMETIC 

Table  of  Aliquot  Parts 


Nos. 

I's 

i'« 

i's 

tVs 

fs 

rs 

iV's 

iVs 

i's 

rVs 

1 

.50 

.25 

.12^ 

.06^ 

.33i 

M6| 

.08^ 

.061 

.20 

.10 

10 

5. 

n 

U 

.621 

^ 

If 

.83^ 

.66f 

2. 

1. 

ICO 

50. 

25. 

m 

6i 

m 

16f 

8^ 

6f 

20. 

10. 

1000 

500. 

250. 

125. 

62^ 

33.3^ 

166| 

83i 

66| 

200. 

100. 

WRITTEN  EXERCISE 

In  the  three  problems  following  make  all  the  extensions  mentally/. 

1.  Without  copying,  find  quickly  the  total  cost  of : 
84  lb.  tea  at  50^.  6^  lb.  tea  at  64:^. 

75  lb.  tea  at  331^.  25  lb.  cocoa  at  52^. 

72  lb.  coffee  at  25^.  121  lb.  cocoa  at  48^. 

84  lb.  coffee  at  331^.  360  lb.  codfish  at  6|^. 

25  lb.  coffee  at  28^.  66  lb.  crackers  at  8^^. 

88  lb.  candy  at  121^.  25  lb.  chocolate  at  36^. 

24  lb.  tapioca  at  6|^.  25  cs.  horseradish  at  64  f^. 

2.  Without  copying,  find  quickly  the  total  cost  of : 


25  yd.  silk  at  84^. 
12^  yd.  silk  at  96^. 
750  pc.  lace  at  6J^. 
112  yd.  ticking  at  6-J^. 
210  yd.  plaids  at  331^. 
128  gro.  buttons  at  12i^. 
68  yd.  lansdowne  at  50^. 


77  yd.  duck  at  142^. 

6{  gro.  buttons  at  S2^. 

155  yd.  cheviot  at  20^. 

96  yd.  gingham  at  8J^. 

84  yd.  shirting  at  12|^. 

25  doz.  spools  thread  at  25^. 

168  yd.  striped  denim  at  8^  ^. 


3.    Without  copying,  find  quickly  the  total  cost  of 


25  bu.  corn  at  64^. 
25  bu.  corn  at  $0.72. 
121  bu.  oats  at  10.36. 
25  bu.  beans  at  12.80. 
121  bu.  wheat  at  11.04. 
121  bu.  millet  at  11.24. 
25  bu.  clover  seed  at  i3.60. 
50  bu.  clover  seed  at  13.75. 


25  bu.  corn  at  10.84. 

25  bu.  corn  at  10.44. 

25  bu.  oats  at  $0.35. 

12Jbu.  rye  at  f  1.04. 

6 J  bu.  wheat  at  $1.20. 

6Jbu.  wheat  at  11.12. 

25  bu.  timothy  seed  at  $2.40. 

60  bu.  timothy  seed  at  $2.75. 


ALIQUOT  PARTS  161 

ORAL  EXERCISE 

1.  Multiply  by  10:  4;  15;. 07;  8^;  11.12;  $24.60;  112.125. 

2.  Multiply  by   100:    3;   17;     .09;    12^;    11.64;    121.17. 

3.  Multiply  by  1000:  7;    29;    .19;    15^;  $1.75;    123.72. 

4.  What  aliquot  part  of  1 10  is  12.50  ?     Find  the  cost  of  16 
articles  at  110  each;  at  $2.50  each. 

5.  Find  the  cost  of  84  bu.  of  wheat  at  f  1.25. 

Solution.    $1.25  is  \  of  $10.  84bu.  at  $10  =  $840;  |  of  $840  =  $105. 

6.  Formulate  a  short  method  for  finding  the  cost  when  the 
quantity  is  given  and  the  price  is  $1.25. 

Solution.   $1.25  is  ^  of  $10;  hence,  multiply  the  quantity  by  10  and  take  \ 
of  the  product. 

7.  Formulate  a  short  method  for  finding  the  cost  when  the 
quantity  is  given  and  the  price  is  $2.50;  $3. 33 J;    $1.66|. 

8.  Find  the  cost  of  168  yd.  of  cloth  at  $1.25;  at  $2.50; 
at  $3,331;  at  $1.66|. 

9.  What  aliquot  part  of  $100  is  $25?    $12.50?   $6.25? 

10.  Find  the  cost  of  72  chairs  at  $25  each. 

Solution.    72  chairs  at  $100  =  $7200;  but  the  price  is  $25,  which  is  \  of 
$100  ;  therefore,  \  of  $7200,  or  $1800,  is  the  required  cost. 

11.  Give  a  short  method  for  multiplying  any  number  by  25 ; 
by  121;  by  61;  by  33^;  by  81 

12.  Find  the  cost  of  25  T.  coal  at  $7.20 ;  of  6 J  T. ;  of  121  T. 

13.  What  aliquot  part  of  1000  is  250  ?    500  ?    125  ?    621  ? 
3331?    I66f?    200?    100?    83i  ?    66|? 

14.  Formulate  a  short  method  for    multiplying  a    number 
by  250. 

Solution.  Since  250  =  ^^^-^^  multiply  by  1000  and  take  J  of  the  product. 

15.  Give  a  short  method  for  finding  the  cost  when  the  quan- 
tity is  given  and  the  price  is  $125 ;  $166|. 

16.  Multiply  84  by  50 ;  by  25 ;  by  121;  by  16|;  by  331 

17.  Multiply  160  by  21;  bylj;  by  121;  by  125;  by  621 

18.  Multiply  240  by  3};  by  1|;  by  331;  by  16f ;  by  3331. 


162  PRACTICAL   BUSINESS  ARITHMETIC 

19.  Find  the  cost  of  250  sofa  beds  at  132  each. 

Solution.  The  cost  of  250  beds  at  $32  =  the  cost  of  32  beds  at  $  250,  The 
cost  of  32  beds  at  $1000  =  $32,000  ;  but  the  price  is  $250,  which  is  |  of  $1000; 
therefore,  ^  of  $32,000,  or  $8000,  is  the  required  cost. 

20.  Find  the  cost  of  720  couches  at  $12.50  each. 

21.  Find  the  cost  of  440  lb.  sugar  at  2^j^. 

Solution.  2^^  is  ^  of  10^.  The  cost  of  440  lb.  at  10^  =  $44 ;  but  the  price  is 
2|^,  therefore,  I  of  $44,  or  $11  =  the  required  cost. 

22.  Formulate  a  short  method  for  finding  the  cost  when  the 
quantity  is  given  and  the  price  is  1|^. 

Solution.  l\f  =  ^  oilOf;  hence,  point  off  one  place  in  the  quantity  and  take 
I  of  the  result. 

23.  Give  a  short  method  for  finding  the  cost  when  the  quan- 
tity is  given  and  the  price  is  2|-^;  3J^  ;  IJ^. 

24.  Find  the  cost  of  160  lb.  at  2|^;  at  11^;  at  SJ^; 
at  1|^.     Also  of  240  lb.  at  each  of  these  prices. 

25.  Find  the  cost  of  2400  lb.  at  2^;  at  1^^;  at  3|^; 
at  1|^.     Also  of  360  lb.  at  each  of  these  prices. 

ORAL    EXERCISE 

Bi/ inspection  find  the  cost  of  : 

1.  25  lb.  tea  at  54^.  16.  Hyd.  silk  at  88^. 

2.  25  lb.  tea  at  33^^.  17.  64  pc.  lace  at  11.25. 

3.  125  lb.  tea  at  64^.  18.  125  yd.  silk  at  11.12. 

4.  6|  A.  land  at  8112.  19.  1250  bbl.  beef  at  $24. 

5.  25  T.  coal  at  18.40.  20.  78  yd.  velvet  at  $2.50. 

6.  25  T.  coal  at  15.20.  21.  2^  bu.  potatoes  at  96^, 

7.  18  T.  coal  at  16.25.  22.  640  bu.  apples  at  871^. 

8.  164  A.  land  at  125.  23.  840  yd.  prints  at  16|^. 

9.  72  T.  coal  at  16.25.  24.  121  bu.  potatoes  at  64:^. 

10.  250  yd.  silk  at  88^.  25.   84  bookcases  at  112.50. 

11.  250  yd.  silk  at  96^.  26.  810  bbl.  pork  at  112.50. 

12.  25  pc.  lace  at  16.60.  27.  125  yd.  crepon  at  $3.60. 

13.  250  yd.  silk  at  $1.12.  28.  12^  yd.  cheviot  at  $1.04. 

14.  192  A.  land  at  $12.50.  29.   24  oak  sideboards  at  $125. 

15.  165  gro.  buttons  at  33lj^.  30.  121  yd.  gunner's  duck  at  48^. 


ALIQUOT  PAETS  163 


WRITTEN   EXERCISE 


In  the  following  problems  make  all  the  extensions  mentally.    See 
how  many  of  the  problems  can  be  done  in  10  minutes. 
1.    Without  copying,  find  the  total  cost  of  : 


425  lb.  at  10  ^. 

2500  1b.  at  64/. 

24  1b.  atl^/. 

310  lb.  at  20  ^. 

1600  1b.  at  25/. 

48  1b.  at  21/. 

100  lb.  at  14  ^. 

1893  1b.  at  31/. 

2i'lb..at96/. 

1000  lb.  at  27 1 

2500  1b.  at  14/. 

125  1b.  at  24/. 

1000  1b.  at  41^. 

1400  1b.  at  25/. 

192  lb.  at  31  /. 

1250  lb.  at  44  ^. 

1250  1b.  at  88/. 

88  1b.  at  121/. 

2.    Without  copying,  find  the  total  cost 

of: 

88  yd.  at  11  A 

174   yd.  at  10^. 

24  yd.  at  12  /. 

72  yd.  at  31^. 

123   yd.  at  11/. 

78  yd.  at  31/. 

104  yd.  at  21  ^. 

127   yd.  at  11/. 

165  yd.  at  20  /. 

480  yd.  at  6|  ^. 

246   yd.  at  25/. 

114  yd.  at  6f/. 

360  yd.  at  81 A 

.1712  yd.  at  10/. 

1280  yd.  at  61/. 

121  yd.  at  11  ^. 

1783  yd.  at  10/. 

192  yd.  at  33 J/. 

3.    Copy  and  find  the  total  cost  of  : 

450  1b.  ut  11^. 

249  1b.  at  25/. 

6J  lb.  at  88  /. 

820  1b.  at  11/. 

240  1b.  at  31/. 

92  1b.  at  21/. 

1200  1b.  at  41/. 

200  1b.  at  31/. 

121  lb.  at  24  /. 

1400  lb.  at  61  /. 

450  1b.  at6f/. 

18  lb.  at  41  /. 

7961  lb.  at  50  /. 

791  lb.  at  40/. 

1251b.  at  18/. 

1293  lb.  at  30  /, 

7811b.  at  50/. 

648  1b.  at  61/. 

1480  lb.  at  40  /. 

750  1b.  at  331/. 

1900  1b.  at  4J/. 

4.    Copy  and  find  the  total  cost  of  : 

750  gal.  at  81  /. 

99  gal.  at  30  /. 

360  gal.  at  5  /. 

488  gal.  at  6|  /. 

60  gal.  at  ^  /. 

625  gal.  at  64/. 

640  gal.  at  61  /. 

50  gal.  at  76/. 

810  gal.  at  11/. 

194  gal.  at  50/. 

25  gal.  at  74/. 

920gal.  at  21/. 

176  gal.  at  25  /. 

121  gal.  at  88  /. 

165  gal.  at  6|  /. 

280  gal.  at  121^. 

79  gal.  at  331/. 

240  gal.  at  621  ^ 

720  gal.  at  331/. 

20  gal.  at  $1.79. 

666  gal.  at  66f  /. 

366  gal.  at  16f  j^. 

6^  gal.  at  $1.96. 

1680gal.  at  16f/. 

164  PEACTICAL  BUSINESS  ARITHMETIC 

ORAL  EXERCISE 

1.  How  much  less  than  fl  is  75^?  what  fractional  part 
of  II  less? 

2.  Find  the  cost  of  144  pc.  of  lace  at  75  P  per  piece. 

Solution,     At  $  1  per  piece  the  cost  would  be  $  144  ;  but  the  cost  is  not  $  1 
but  I  less  than  $  1.    Deducting  ^  of  $  144,  the  result  is  $  108,  the  required  cost. 

3.  Find  the  cost  of  124  bookcases  at  $7.50. 

Solution.     $  7.50  is  ^  less  than  $  10.    $  1240  less   {  of   itself  =  $  930,  the 
required  result. 

4.  Formulate  a  rule  for  multiplying  a  number  by  .75;  by 
7J;  by  75;  by  750. 

5.  How  much  more  than  il  is  $1.12^7  What  fractional 
part  of  $  1  more  ? 

6.  Find  the  cost  of  84  yd.  of  silk  at  |1.16|  per  yard. 

Solution.     At  $  1  per  yard,  the  cost  would  be  $84;  but  $1.16|  is  ^  more 
than  $1.     Adding  ^  of  $84  to  itself,  the  result  is  $98,  the  required  cost. 

7.  Formulate  a  short  method  for  finding  the  cost  when 
the  quantity  is  given  and  the  price  is  1 1.12 J;  $1.16 J; 
|1.33i;  $11.25;  1112.50. 

8.  How  much  less  than  $1  is  87|^?  what  fractional 
part  of  f  1  less  ?  Formulate  a  short  method  for  multiplying  a 
number  by  87-^. 

9.  Formulate  a  short  method  for  multiplying  a  number 
by  .831;  by  1.25. 

10.    Compare  the  cost  of  Sl^  yd.  at  64^  with  the  cost  of 
64  yd.  at  87^^. 

ORAL  EXERCISE 

State  the  cost  of: 

1.  24  yd.  at  75  P.  7.  87^  yd.  at  $  2.88.  13.     270  yd.  at  111  ^. 

2.  75  yd.  at  24  ^.  a     25  yd.  at  4  ^.       14.     144  yd.  at  1 1^  ^. 

3.  192  yd.  at  871^.  9.  28  yd.  at  75^.  15.  Iliyd.atl8^. 

4.  240  yd.  at  83|  P.  10.  27  yd.  at  75^.  16.  1125  yd.  at  64^. 

5.  871  yd.  at  $2.48.  u.  75yd.at84^.  17.  1125  yd.  at  32^. 

6.  176  yd.  at  $1,121  12.  75  yd.  atl6f^.  18.  1125 yd.  at  48^. 


ALIQUOT  PAETS 


165 


WRITTEN  REVIEW  EXERCISE 

1.  Find  the  total  of  the  costs  called  for  in  problems  1-15  in 
the  oral  exercise  at  the  top  of  page  159. 

2.  Find  the  total  cost  of  the  items  in  the  oral  exercise  at  the 
bottom  of  page  162;  of  the  items  in  the  oral  exercise  at  the 
bottom  of  page  164. 

3.  Find  the  total  cost  of  : 

84  yd.  at  7^.  98  yd.  at  9^. 

1121yd.  at  5^.  79  yd.  at  11^. 

1121yd.  at  6^.  17  yd.  at  16^. 

4.  Find  the  total  cost  of : 
71  yd.  at  22^.  85  yd.  at  30^. 
31  yd.  at  44^.  17  yd.  at  25^. 
82  yd.  at  88  jz^.               121  yd.  at  39^. 
71  yd.  at  12  f.               250  yd.  at  64^. 

5.  Find  the  total  cost  of  : 
192  lb.  at  31^.  167  lb.  at  121^. 
3841b.  at  6|^.  184  lb.  at  371^. 


72  yd.  at  75^. 
871yd.  at  88^. 
320  yd.  at  11^. 

30  yd.  at  71^. 
24  yd.  at  81  f^. 
56  yd.  at  831^. 
124  yd.  at  $1,121 

1151f  lb.  at  10^. 


172111b.  at  15^. 


378  1b.  at  61  P. 
149  1b.  at  6 J  f^. 


2164  1b.  at  2|^. 
1369  lb.  at  21^. 


291111b.  at  331^. 
2706  lb.  at  331^. 


6.   Copy  and  find  the  amount  of  the  following  bills,  less  3  % 

a. 

Rochester,  N.Y.,  Aug.  2,  19 


Mr.  C.  G.  Garlic 

North  Rose,  N.Y. 


To  Smith,  Perkins  &  Co.,  Dr. 


Terms  :  cash,  less  3  %. 

330  lb.  Granulated  Sugar 

6^^ 

32   «   Butter 

22^ 

64   "  Cheese 

161^ 

75   "   Young  Hyson  Tea 

24^ 

155   "   Dried  Apples 

^^ 

300   "   Brown  Sugar 

H^ 

60   "   Oolong  Tea 

51^ 

125  «   Rio  Coffee 

28^ 

250   "   Mocha  Coffee 

24  j* 

166 


PRACTICAL   BUSINESS  ARITHMETIC 


h. 


Buffalo,  N.Y.,  Aug.  5, 19 


Mr.  George  A.  Collier 

Savannah,  N.Y. 

Bought  of  George  H.  Buell  &  Co. 

Terms :  cash,  less  3  %. 


72  pr.  Boys'  Hose  12^^ 

18  doz.  Linen  Handkerchiefs  2.50 

18    "      Lace  Handkerchiefs  3.33^ 

78  yd.  Silk  Velvet  3.33^ 

75  pc.  Black  Ribbon  28^ 

347  yd.  Pontiac  Seersucker  Q\^ 

186   "    Washington  Cambric  12^^ 


ORAL  EXERCISE 

1.  At  33^  ^  per  pound,  how  many  pounds  of  coffee  can  be 
bought  for  $12? 

Solution.  .33^  =  $  i  ;  3  pounds  can  be  bought  for  $  1 ;  then,  12  x  3  lb. 
=  36  lb.,  the  required  result. 

2.  When  the  cost  is  given  and  the  price  is  25^,  how  may 
the  quantity  be  found? 

Solution.  When  the  price  is  25  ^,  the  quantity  is  4  times  the  cost ;  hence, 
multiply  the  cost  by  4- 

3.  Give  a  short  method  for  finding  the  quantity  when  the 
cost  is  given  and  the  price  is  20^;  33^^;  12^^;  6^^;  6|^; 
16|^. 

4.  Formulate  a  short  method  for  dividing  any  number  by 
125. 

Solution.  125  is  \  of  1000  ;  then  the  quotient  by  125  will  be  8  times  the 
quotient  by  1000.  Therefore,  divide  by  1000  and  multiply  the  result  by  S.  Or, 
tI?  =  ttjW-  Therefore,  multiply  by  8  and  move  the  decimal  point  three 
places  to  the  left. 

5.  Give  a  short  method  for  dividing  by  6J. 

Solution.  6^  =  -^  of  100  ;  then  the  quotient  by  Q\  -will  be  16  times  the 
quotient  by  100.  Therefore,  move  the  decimal  point  two  places  to  the  left  and 
multiply  the  result  by  16.  Or,  i  =  ^^^.  Therefore,  multiply  by  16  and  move  the 
decimal  point  two  places  to  the  left. 


ALIQUOT   PARTS 


16^ 


16|; 


6.  Give  a  short  method  for  dividing  a  number  by  12|  ;  by 
by  33J  ;  by  6^  ;  by  66| ;  by  333|.;  by  166|. 

7.  Formulate  a  short  method  for  dividing  a  number  by  .75. 

Solution.  .75  increased  by  |  of  itself  =  1.  When  the  divisor  is  1  the  quo- 
tient is  the  same  as  the  dividend.  Hence,  to  divide  a  number  by  .75  increase 
the  number  by  ^  of  itself. 

8.  At  75  ^  per  bushel,  how  many  bushels  of  wheat  can  be 
bought  for  .t?144?  for  1192?  for  $240?  for  1780?  for  |1260? 
for  1 360?  for  $1350?  for  $810? 

9.  At  $7.50  per  dozen,  how  many  dozen  men's  gloves  can 
be  bought  for  $1440? 

Solution,  f  7.50  +  ^  of  itself  =  $10.  To  divide  by  10  is  to  point  off  one 
place  to  the  left.  $  1440  +  |  of  itself  =  $1920  ;  $  1920  ~  $  10  =  192,  the  number 
of  pairs  of  gloves. 

10.  State  a  short  method  for  dividing  a  number  by  7^  ;  by 
75 ;  by  750. 

ORAL    EXERCISE 
Find  the  quantity: 


Price  per 

Price  per 

Cost 

Yard 

Cost 

Pound 

1.    $65 

331^ 

7.    $75 

6|^ 

2.    $250 

25^ 

•   8.    $12 

1|^ 

3.    $120 

H^ 

9.    $25 

n^ 

4.    $215 

2|^ 

10.    $38 

H^ 

5.    $126 

12|^ 

11.    $125 

$1.25 

6.    $125 

20^ 

12.    $420 

12^^ 

WRITTEN   EXERCISE 


Find  the  quantity : 


Price  per 

Price  per 

Cost 

Yard 

Cost 

Bushel 

1. 

$570.00 

75^ 

6. 

$1721.00 

88i** 

2. 

$612.00 

75>^ 

7. 

$1842.50 

25^ 

3. 

$274.50 

n^ 

8. 

$1785.00 

8Yi^ 

4. 

$281.50 

v^\i 

9. 

$2142.00 

zz\t 

5. 

$864.50 

121^ 

10. 

$2720.50 

16|^ 

168 


PRACTICAL   BUSINESS   ARITHMETIC 


REVIEW    EXERCISE 

This  exercise  may  be  used  in  a  number  of  different  ways,  some  of  which 
are  suggested  below. 

1.  One  student  may  make  the  oral  extension,  using  the  first  quantity, 
60  yd.,  by  each  price  in  column  1 ;  a  second  student  may  use  the  same 
quantity  and  make  the  extension  by  each  price  in  column  2,  and  so  on  for 
the  ten  lists. 

2.  Each  student  in  the  class  may  take  the  same  quantity  and  make  the 
extension  by  each  price  in  column  1,  and  foot  the  extensions.  Compare 
results.  Such  an  exercise  should  occupy  one  minute.  This  work  may  be 
continued  for  ten  or  fifteen  minutes  daily,  as  the  instructor  desires,  a  different 
quantity  being  used  for  each  minute. 


1 

8 

3 

4 

5 

6 

7 

8 

9 

10 

50/ 

25/ 

66f/ 

60/ 

25/ 

6i/ 

50/ 

75/ 

$1.50 

$1,331 

20/ 

62^/ 

6|-/ 

87^/ 

20/ 

16f/ 

90/ 

81/ 

$1.25 

$1.66§ 

12i/ 

331/ 

75/ 

37^/ 

60/ 

30/ 

10/ 

371/ 

$1,121 

$1.20 

16f/ 

30/ 

H^ 

6i/ 

12^/ 

66f/ 

62^/ 

80/ 

$1.10 

$1.16§ 

90/ 

10/ 

40/ 

80/ 

331/ 

6f/ 

40/ 

87^/ 

$1.75 

$1.30 

1.  Find  the  cost  of : 


a.  60  yd. 
80  yd. 
40  yd. 


b.  72  yd. 
50  yd. 
44  yd. 


90  yd. 
20  yd. 
25  yd. 


d.  75  yd. 
84  yd. 
54  yd. 


48  yd. 
96  yd. 
64  yd. 


2.  Find  the  cost  of 


a.  24  yd. 
16  yd. 
32  yd. 


h.  78  yd. 
69  yd. 
81yd. 


12  yd. 
36  yd. 
42  yd. 


d,  92  yd. 
21yd. 
46  yd. 


15  yd. 
18  yd. 
10  yd. 


3.  Find  the  cost  of 


a.  100  yd. 
120  yd. 
150  yd. 


h,  108  yd. 
135  yd. 
144  yd. 


e.  160  yd. 
180  yd. 
128  yd. 


d.  200  yd. 
240  yd. 
300  yd. 


320  yd. 
400  yd. 
360  yd. 


ALIQUOT   PAliTS 

WRITTEN    REVIEW    EXERCISE 


169 


Name 

Quan- 
tity 

Prices 

1 

2 

3 

4 

6 

6 

Boucle  Stripe 

yd. 

10.104 

$0.11 

$0.10 

$0,114 

$0.12 

$0,124 

Dress  Silks 

yd- 

1.20 

1.25 

1.33^ 

1.374 

1.40 

1.50 

English  Serge 

yd. 

1.33^ 

1.30 

1.35 

1.25 

1.374 

1.45 

Fancy  Gingham 

yd. 

.061 

.06 

.064 

.07 

.074 

.071 

Fancy  Plaids 

yd. 

.3H 

.32 

.331 

.35 

.34 

.374 

Gunner's  Duck 

yd. 

.14 

.15 

•144 

.16 

.17 

.174 

Percale  Shirting 

yd. 

.07 

.071 

.08 

.084 

.09 

.094 

Scotch  Cheviot 

yd. 

.39 

.40 

.371 

.45 

.44 

.48 

Taffeta  Silk 

yd. 

.874 

.85 

.90 

.88 

.921 

.95 

Wash  Silk 

yd. 

.30 

.374 

.40 

.35 

.42 

.414 

Prepare  each  of  the  following  invoices  in  correct  form^  omit  the 
headiiig^  and  find  the  value  hy  each  price  list. 


3. 


22  3^d.  Boucle  Stripe 

2.    72  yd.  Dress  Silk 

27  yd.  English  Serge 

.     104  yd.  Scotch  Cheviot 

56  yd.  Percale  Shirting 

64  yd.  Taffeta  Silk 

48  yd.  Wash  Silk 

60  yd.  Gunner's  Duck 

36  yd.  Fancy  Gingham 

4.    96  yd.  Fancy  Plaids 

88  yd.  Scotch  Cheviot 

36  yd.  English  Serge 

92  yd.  Wash  Silk 

100  yd.  Taffeta  Silk 

120  yd.  Boucle  Stripe 

70  yd.  Percale  Shirtuig 

80  yd.  Gunner's  Duck 

90  yd.  Wash  Silk 

72  yd.  Boucle  Stripe 

6.    84  yd.  Taffeta  Silk 

56  yd.  Wash  Silk « 

QQ  yd.  Fancy  Gingham 

50  yd.  Fancy  Plaids 

84  yd.  Scotch  Cheviot 

80  yd.  Dress  Silk 

Q^  yd.  English  Serge 

70  yd.  Gunner's  Duck 

45  yd.  Percale  Shkting 

CHAPTER   XIV 

BILLS  AND  ACCOUNTS 
BILLS 

203.  A  detailed  statement  of  goods  sold,  or  of  goods  bought 
to  be  sold,  is  called  either  a  bill  or  an  invoice.  A  detailed  state- 
ment of  goods  bought  to  be  used  or  consumed,  such  as  office 
furniture,  stationery,  and  fuel,  or  a  statement  of  services  ren- 
dered, or  of  a  work  performed,  is  called  a  bill. 

Thus,  a  physician's  statement  of  services  rendered,  or  a  transportation 
company's  bill  for  work  performed,  and  the  charges  for  the  same,  is  called  a 
hill;  but  a  statement  of  a  quantity  of  silk  bought  or  sold  by  a  dry-goods 
merchant  in  the  course  of  trade  is  called  either  a  hill  or  an  invoice, 

204.  The  models  following  show  a  variety  of  current  prac- 
tices in  billing.    They  will  therefore  be  found  helpful  as  studies. 

1.   Groceries 
Boston,  Mass.,         Oct.    15,         19 

Messrs.   SMITH,    PERKINS  &  CO. 

Rochester,    N.Y. 

Bought  of  E.  E.  GRAY  COMPANY 


Terms  30  da. 


Telephone,  Main  167 


bbl.    Rolled  Oats 

"   Gold  Medal  Flour 
bx.  Wool  Soap 


$6 .  25 
6.50 
3.10 


18 
65 
15 


75 

00 
50 


99 


25 


This  is  one  of  the  simplest  bill  forms;  it  is  the  form  that  is  common 
in  a  great  many  lines  of  business. 

170 


BILLS   AND  ACCOUNTS 


171 


2.   Groceries 

on.  Mass.,         Nov.    12,  19 

Messrs.   E.    0.    Sherman  &  Co. 

Charlestown,   Mass. 

Bought  of  S.  S.  PIERCE  COMPANY 

Terms  30  da.;  3fo  10  da. 


10  Red  Label  Hams  146  lb. 
20  mats  Java  Coffee  1500  " 
12  6-lb.  tins  Mustard  72  « 
15  6-lb.  tins  Cocoa     90   " 


$0.23   $33.58 

.25   375.00 

.36   25.92 

.34   30.60 

$465.10 


Goods  bought  by  the  mat,  chest,  case,  etc.,  are  frequently  billed  by  the 
pomid.     The  above  bill  shows  the  form  in  such  cases. 

3.    Hardware 

The  following  bill  is  sometimes  used  in  the  hardware  business.  The  first 
number  after  the  name  of  the  article  is  the  quantity ;  the  number  above  the 
horizontal  line  following,  the  price ;  and  the  number  below  the  line,  the  grade. 
Thus,  the  first  item  in  the  bill  shows  that  12  doz.  porcelain  knobs  in  all  were 
sold,  of  which  6  doz.  were  No.  8  at  ^1.25  and  6  doz.  No.  16  at  $1.33J. 


JTeu,  York.- 


(W^Jz-^.    C, 19 


^.^LA^^^LA. 


bought  of  Cf/ie  Eureka   hardware  Qompani^ 


A^. 


Q^^^^^^.^^.^ 


/^^ 


/  C  / 


z^ 


Iz^ 


zj: 


172 


PEACTICAL   BUSINESS  ARITHMETIC 


4.   Wholesale  Dry  Goods 


M^^^^^ 


CHICAGO. /V^^^^^-  /.^  10 


-i<2../j^y^  T^^a^ 


TERMS-^22^^^^^ 


Bought  of  MARSHALL  FIELD  &  CO. 

Franklin  Street  and  Fifth  Avenue 


/2.^ 


Z^ 


^^'1^^^^^^ 


jiLL ^J     ^/'     ¥^^     ^O'  ^Z 


^atp J3'A  ' /^.C 


^ 


JLZJL 


J^ 


J (7    3  2.^     14^'    ¥/^    3<?'    ¥a 


JL2^ 


L2. 


■^^^g^  ^.^fT-YlySYy-j-?^--^^)^^^^^  ^^ 


4^2^ 


'■  2-^f^ 


1/.0     Jf     ¥2.      ¥o     ¥i.     ¥a 
¥1.    ^/     /^i.      <^/     ^j      ^3 


/JZ 


A^jT  ^^<'    ^/ 


ZS 


jL2^ 


'■/    ¥3    Vi.    -/y     ^J    ^f 

^:L      A^a      4^/>      ^2^       ^^      <A/ 


±2^ 


IZ. 


/  J/  t  ^/7         c£-/i         ZZ/9         Z^.  ?         9^^ 


¥ft  J/^. 


JJ^ 


TJi 


<^£2=22^ 


//.Z.      ^O      ^^f      A^O      A^3 

y/     z^3    ¥C    .^^    ¥^   ^J^ 


^f     C%^ 


^lA 


^ 


/J^ 


^^^  '-^^^:^^^^^^:^&^^^</^ 


^7    "^z  ^f-  ¥/^37  ¥X 


2.^s-   /// 


2JL 


zz 


/^/ 


-'^^l-t^.(y/^'.A^^<>-?^'y:iC- 


J^   ¥/'  ^^-^  ¥C  W  ¥3 


a!C^7^:7y/^..^^^^^-r^-y7  ^  ^ 


J^Ll—^^ 


2.ro 


Z2. 


/«<7 


i:^f?^,^^>-ir(^'/-Air^n^i^i^r?'i^^  ^/^ 


2^\ 


m 


££0. 


;Z£ 


In  the  wholesale  dry-goods  business  the  price  is  generally  for  a  yard,  and 
the  number  of  yards  to  the  piece  varies  in  some  kinds  of  cloth.  The  first 
item  in  the  above  bill  is  followed  by  a  series  of  numbers,  41,  42,  etc. ;  these 
represent  the  number  of  yards  in  each  of  the  12  pc.  Immediately  following 
these  numbers  is  recorded  the  total  number  of  yards  in  the  12  pc.  The 
total  number  of  yards  should  be  found  by  horizontal  addition. 

5.   Manufacturer's 

The  following  is  a  bill  for  neckwear.  The  different  styles  are  distin- 
guished by  the  marks  at  the  left  of  the  quantity.  This  form  is  common 
among  manufacturers,  jobbers,  and  wholesalers.  Bills  on  which  trade 
discounts  (sefe  page  246)  are  allowed  are  arranged  as  shown  in  this  bill. 


BILLS  AKD  ACCOUNTS 


173 


BetoP0rlt,        Oct.   10,        19 

,essrs.  J.  E.  Whiting  &  Co. 

Boston,  Mass. 

^ongfyt  of  2Pol)u^on  ^ttx^.y  M>on^  S.  €o* 

Cermfli  Net  30  da. 


721 

n 

1026 

1 

2 

1025 

1^ 

1020 

3 
4 

923 

2J 

1015 

li 

doz.    Neckwear 


Less  25s 


$4.50 

6 

75 

27.00 

13 

50 

27.50 

41 

25 

9.00 

6 

75 

18.00 

45 

00 

24.00 

42 

00 

155 

25 

3 

11 

152 

14 


6.   Furniture 


In  the  following  bill  the  goods  were  sold  delivered  on  the  cars  (f.  o.  b.) 
Boston,  but  the  shippers  prepaid  the  freight  to  Bangor.  The  freight  is  a  part  of 
the  selling  price  and  is  added  to  the  amount  of  the  bill,  as  shown  in  the  model. 


yi..£.<£dLLJL 


^j^;;^. 


BOSTON,. 


K^^w^ 


2=^ .9 — 


^^^'■f^TL.-r^t'^r?-'^^ 


.^ 


Bought  of  E.   M.  PRAY,  SONS  &  CO. 

^o  Manufacturers  of  Fine  Furniture 

TERMS  //C^J^^-1^^ 


AJl. 


./T 


^^yfJi^^-<^^A^1^?r^^^^ 


Ll^ 


7^- 


^ 


^^^22^^;2^:^2l^^,i^^^^^-2Z-^^L^^l;^^ 


r/0 


174 


PRACTICAL   BUSINESS  ARITHMETIC 


7.   Wholesale  Coal 
F.  H.  OSBORN  &  CO. 

SHIPPERS  OF 

Anthracite,   Bituminous,  and  Qas  Coal 


Sold  to  Y^.Jfp^^T^J-^^^^  r^f^, 


c^r?-?^.  Aff 


.I9_ 


Terms 


'-yy^A^^ 


/^ Z  ^/^^^^^^^y-C7^^^i,^d^^.  ^^^ 


r 


27  tr? ^  ^-^^^yj>. 


oT-i 


^5-0 


^(^^g:^^^'?€^y 


.^^ 


AJ7 


X^ 


l0Ai2J2J^t^H^ 


^222^2^ 


M~££ 


-/^ 


Xf  y  o  r?^  ,^^^^^^^^ 


2=£L 


S3_ 


^^^^^.^C^/-^^--^^i^a^y^-?^^.^yr^^ 


^^^^n^^^.^^ 


^^^^O^ 


The  above  is  a  form  of  bill  that  is  generally  used  for  wholesale  transactions 
in  coal.  It  is  called  a  receipted  bill,  and  shows  that  the  coal  has  been  paid  for. 


\^yLL 


8.   Retail  Coal 


^ottton,- 


^ 19 


2-/2-  ^^yf.^J^'^^^^^^iCfP-^^  fyf^A-^^y^^J>?. 


Crcrm0- 


Trnm  of  jf.  ia.  C\)mtt  &.  Co. 


T 


2.  -t^r777^^c7^^i<^W7^, 


V?yr^^z7. 


^J^£?-Z/^0     ^JS>0-2./F0  /V/^/?#-      C'- 


J^ 


2^ 


Z^ 


2.  -i^^^T-g?.^^  --^^<^-^^,y9..^:^-r7^^ 


/".JPO-Z/^e?     /'.^^00-2,/^/:^     ^-^OOr^       ^- 


^^ 


i£^ 


_.i:^ 


^ 


/^Y^ 


^m^^^^^^ 


^^-/J/^.- 


BILLS  AND  ACCOUNTS 


175 


The  foregoing  bill  shows  a  form  sometimes  used  by  retailers.  The 
numbers  at  the  left  of  the  hyphen  are  the  gross  weights,  and  the  numbers 
at  the  right  the  tares  of  the  different  loads. 


9.   China  and  Glassware 

^/joston,  Nov.    6, 

^£  THE  WENTWORTH  =  STRATTON   CO. 

Rochester,    N.Y. 


79 


bought  of  Osgood,   Kyraoer  &-  ^ort 

*Jerm^   60  da.  not;  2$  10  da. 


Dinner  Set,  130  pieces;  viz. 

1  doz.  Plates.  8  in.  188  /5^ 

.SJ>' 
1. 13 

.^¥ 
^9 

•  1^ 
SS 
1(0 

,3H 

■  17 

.JO 
J..«-i' 

25  more  Dinner  Seta  as  above  19.07        476  75         7. 

'tTL^     - 

505  42 

The  above  form  is  common  in  the  china  and  glassware  business.     In^thfs.  y^" 
case  a  charge  is  made  for  the  crates  used  in  packing  and  the  prices  do"*nbt' 
include  delivery.     The  cost  of  the  crate  and  the  cost  for  carting  are  there- 
fore made  a  part  of  the  bill. 


1  " 

7  •' 

1  " 

6  •' 

1  •' 

7  *•  (deep) 

1  **   Fruit  Saucers.  4  in. 

1  "   Individual  Butters 

1/12  doz.  Covered  Dishes.  8  i 

1/12   * 

*   Casseroles.  8  in. 

1/4    * 

Dishes,  8  in. 

1/12   • 

10  " 

1/12   * 

12  •• 

1/12   • 

14  *• 

1/6 

Bakers,  8  in. 

1/12   * 

*   Sauce  Boats 

1/12   ' 

*   Pickles 

1/12   * 

*   Bowls 

1/12   * 

*   Sugars 

1/12   ' 

Creams 

1 

Handled  Teas 

1/2    ' 

Coffees 

1/12   ' 

'   Pitchers 

1/12   • 

Covered  Butters  and 

Drainers 

more  Di 

nner  Seta  as  above 

Crates 

Carting 

1 

88 

1 

63 

1 

38 

1 

63 
75 
50 

♦12.00 

1 

00 

13.50 

1 

13 

2.50 

63 

4.50 

38 

7.50 

63 

10.50 

88 

4.50 

75 

4.00 

33 

3.00 

25 

2.00 

17 

6.00 

50 

2.79 

2 

23 
00 

2.33 

1 

17 

6.00 

50 

9.00 

75 

19 

07 

19.07 

476 

495 

'7 

2 

75 
82 
50 
10 

176  PRACTICAL  BUSINESS  AEITHMETIC 

10.    Lumber 
Jhe  7{.  ^.  SSickford  Co. 

68oston,  ^Kass.,  Oct.    8,  79 

Sold  to   L.  A.  Hammond  &  Co. 

Paterson,  N.J. 

J^enms  Pgt .   net  cash;    bal.    in  5  da.   less   iJ^S 


23,289  ft.  \  X  2\  #1  N.  C.  Ceili 

ng 

$18.50  $430.85 

3,520  "    "     2  "  '»    " 

17.00   59.84 

10,307  "   i  X  2l  1  "  "     " 

13.50  139.14 

1,690  "    "     2  "  »»    " 

12.50   21.13 

$650.96 

Less  freight  (45,200  lb. 

at  24F^)   108.48 

$542.48 

Lumber  is  generally  sold  by  the  thousand  feet.  In  the  above  bill  the  goods 
were  sold  free  on  board  cars  (f.  o.  b.)  Paterson,  N.J.,  but  the  shippers  have, 
not  prepaid  the  freight.  They  find  that  these  charges  are  %  108.48  and  deduct 
this  amount  from  the  total  of  the  bill.  In  the  wholesale  lumber  business  the 
prices  quoted  usually  include  the  cost  of  delivery,  and  when  the  freight  charges 
are  not  known  at  the  time  of  making  the  shipment,  they  are  paid  by  the 
consignees  and  deducted  from  the  amount  of  the  bill  on  the  arrival  of  the 
goods.     The  freight  bill  is  then  sent  to  the  shippers  for  credit. 

WRITTEN  EXERCISE 

1.  Study  the  model  bill,  page  170.  Increase  the  price  of 
each  article  25^  and  then  copy  and  find  the  amount  of  the  bill. 

2.  Study  the  first  model  bill,  page  171,  and  then  copy  and  find 
the  amount  of  it  at  the  following  prices:  hams,  27 J^;  coffee, 
23^;  mustard,  Z\^\  cocoa,  39^. 

3.  Study  the  second  model  bill,  page  171,  and  then  copy  and 
find  the  amount  of  it  at  the  following  prices :  porcelain  knobs 
#8,11.121;  #16,11.25;  steelyards  #64,  $11 ;  #17,18.331; 
jack-planes  #14,  |6;  #21,  16.25;  #48,  $6.75. 


BILLS   AND  ACCOUNTS  177 

4.  Apr.  15,  you  bought  of  S.  S.  Pierce  Co.,  Boston,  Mass., 
for  cash:  25  gal.  finest  New  Orleans  molasses  at  48^;  15  gal. 
fancy  sugar-house  sirup  at  49^;  75  lb.  raw  mixed  coffee  at 
29^;  25  lb.  raw  Pan-American  coffee  at  19^;  5  cartons  Fowle's 
entire-wheat  flour  at  39 J ^;  Jbbl.  Franklin  Mills  flour  at  16.75; 
I  bbl.  pastry  flour  at  15.25.     Write  the  bill. 

5.  Mar.  19,  Frank  M.  Richmond  &  Co.,  New  York  City, 
sold  to  Charles  M.  Thompson,  Poughkeepsie,  N.Y.,  12  doz.  por- 
celain knobs:  3  doz.  #71  at  16.35,  9  doz.  #74  at  $6.75;  12 
doz.  shingle  hatchets:  6  doz.  #16  at  19.75,  6  doz.  #34  at 
112.50;  7  doz.  steel  squares:  3  doz.  #91  at  $35,  4  doz.  #73 
at  133.     Terms:  30  da.     Write  the  bill. 

6.  Study  the  model  bill  on  page  172.  Increase  the  prices 
of  the  articles  marked  124  and  132  five  cents  each  and  the  re- 
mainder of  the  articles  one  cent  each;  then  copy  and  find  the 
amount  of  the  bill. 

7.  Nov.  15,  J.  B.  Ford  &  Co.,  Albany,  N.Y.,  bought  of  the 
Clinton  Mills,  Little  Falls,  N.Y.,  10  pc.  percale  shirting  con- 
taining 42, 48,  521, 58^  ^2,  38, 49,  51,  54,  and  46^  yd. ,  at  7|  ^ ;  .10  pc. 
fine  wool  cheviot  containing  58^,  42,  49,  51,  442,  43^  43^  412^  39^ 
and  42  yd.,  at  1 1.12 J  ;  5  pc.  cashmere  containing  49^  40^,  48^ 
491,  and  49  yd.  at  $1.37 J.  Terms:  60  da.,  or  3%  discount 
for  cash  within  10  da.     Write  the  bill. 

8.  Study  the  first  model  bill  on  page  173.  Increase  the 
prices  of  styles  1026,  1025,  1020,  and  923,  25^  each  and 
diminish  the  prices  of  the  other  styles  25^  each;  then  copy 
and  find  the  amount  of  the  bill.    Omit  the  discount. 

9.  Sept.  24,  Geo.  W.  Fairchild,  Buffalo,  N.Y.,  bought  of 
E.  M.  Lawrence  &  Co.,  New  York  City,  silk  ribbon  as  follows  : 
12  pc.  #1142  at  $2.25;  5  pc.  #1321  at  $1.25;  25  pc.  #171 
at  $4,371;  8  pc.  #  1927  at  $1.75  ;  36  pc.  #2114  at  $1.66f ;  15 
pc.  #1371  at  $1.33J;  15  pc.  #624  at  $4.371 ;  12  pc.  #909  at 
$1,871;  25  pc.  #1008  at  $3,331;  25  pc.  #1246  at  $4.75;  18 
pc.  #2119  at  $1,121  Terms:  30  da.,  or  2%  discount  for  cash 
in  10  da.     Write  the  bill. 


178  PRACTICAL   BUSINESS  ARITHMETIC 

10.  Study  the  second  model  bill  on  page  173.  Increase  the 
price  of  the  articles  marked  Q5  and  396,  25^  each,  and  diminish 
the  price  of  the  other  articles  12|^  each;  then  copy  and  find 
the  amount  of  the  bill.     Freight  added,  $14.70. 

11.  July  20,  The  Hayden  Furniture  Co.,  Rochester,  N.Y., 
bought  of  John  H.  Pray  &  Son,  Boston,  Mass.,  25  #31  card 
tables  at  111 ;  24  #94  china  closets  at  $27.50 ;  15  #16  dining 
sets  at  $85;  25  #3060  fancy  rockers  at  $9.25;  15  #35  music 
cabinets  at  $2.75;  25  #26  mahogany  office  chairs  at  $12.50; 
12  #89  oak  sideboards  at  $125.  Terms:  30  da.  The  prices 
are  free  on  board  Boston,  and  the  shipper  prepaid  the  freight, 
$34.50.     Write  the  bill. 

12.  Study  the  first  model  bill  on  page  174.  Increase  the 
price  of  the  stove  coal  25^  per  ton  and  the  price  of  each  of  the 
other  kinds  12^^  per  ton;  then  copy  and  find  the  amount  of 
the  bill.     Receipt  the  bill  for  F.  H.  Osborn  &  Co. 

13.  May  19,  C.  E.  Williams  &  Co.,  Cleveland,  O.,  bought  of 
Fairbanks  &  Co.,  Scranton,  Pa. :  3  car  loads  of  stove  coal  weigh- 
ing 20,500,  26,400,  and  25,600  lb.,  respectively,  at  $4.75  per  ton 
(2000  lb.);  1  car  load  grate  coal  weighing  21,900  lb.  at  $4.25  per 
ton;  1  car  load  cannel  coal  weighing  22,500  lb.  at  $7.75  per 
ton.  Terms:  30  da.,  or  3%  discount  for  cash  in  10  da.  Write 
the  bill. 

14.  Study  the  second  model  bill,  page  174,  then  copy  and 
find  the  amount  of  it  at  $6.25  per  ton  for  each  sale. 

15.  Copy  the  bill  in  problem  14  in  accordance  with  the  model 
shown  on  page  174.     Make  the  price  of  the  coal  $6.66|. 

16.  Study  the  model  bill  on  page  175.  Increase  each  price 
given  five  cents  and  then  copy  and  find  the  amount  of  the  bill. 
Cost  of  crates  used  in  packing,  $6.40;  carting,  $2.80. 

17.  July  15,  Henry  Nelson  &  Co.,  Portland,  Me.,  bought  of 
Jones,  Stratton  &  Co.,  New  York  City,  5  doz.  plates,  8  in.,  at 
$1.50;  35  doz.  plates,  7  in.,  at  $1.35;  15  doz.  plates,  6  in., 
at  $1.10;  10  doz.  plates,  5  in.,  at  90^;  65  doz.  handled  teas  at 
$1.85.  Terms:  30  da.  Cost  of  crate  used  in  packing,  $2; 
cartage,  75^.      Write  the  bill. 


BILLS  AND  ACCOUNTS 
STATEMENTS 


179 


FOLIO   7^^ 


Jn  account  with  ^Y^^H^^^.^7^  \-1^^/-^^ 


£:_^-:/^r.^7^^yi-e-. 


^^r?(?   /^ 


ZA 


2.J1 


^^ff 


^2 


'J2. 


np 


W^ 


/ji. 


z^ 


:^ 


w^^C^i^. 


JC^i^-^^ 


J(?C? 


Zi^ 


i^ 


,;// 


i:^ 


^(^7/ 


4A^ 


205.  A  statement  is  an  abstract  of  a  customer's  account,  show- 
ing under  proper  dates  the  details  and  totals  of  debits  and  credits 
and  the  balance  remaining  unpaid. 

Sn  account  with  /CpW^^^  -;^.^^W^^P^-7^/^^-^^ 


Z^ 

z^ 


-/t- 


^^^^^ 


^^.^^?^ 


'^^^^ 


.'<^-^^^-^^<±y^ 


-tM 9^ 


.^.^^. 


-^ ^9- 


'.^^ 


3J2J2. 


2=JL 


il/l 


fe^ 


/otC 


l2^±a, 


-^/^ 


nL 


1=11. 


180 


PEACTICAL  BUSINESS  ARITHMETIC 


The  first  model  on  the  preceding  page  is  a  statement  of  C.  B.  McMeni- 
men's  account  for  January.  It  shows  that  the  charges  aggregate  $997.10, 
the  credits  $671.40,  and  that  the  balance  remaining  unpaid  is  1325.70. 

The  second  model  on  the  preceding  page  is  a  statement  of  C.B.  McMeni- 
men's  account  for  January  and  February.  The  items  on  the  January  state- 
ment are  summarized  in  the  record  "To  account  rendered,  $325.70."  The 
first  item  on  the  March  statement  will  be  "  To  account  rendered,  $412.20." 


WRITTEN    EXERCISE 

1.  During  March,  F.  E.  Smith,  Buffalo,  N.Y.,  bought  mer- 
chandise of  The  Hayden  Furniture  Co.,  Rochester,  N.  Y.,  as  per 
bills  rendered:  namely.  Mar.  3,  $400.80;  Mar.  15,  $360.90; 
Mar.  20,  $200.70;  Mar.  26,  $260.90;  Mar.  28,  $130.50. 
During  the  same  time  he  made  cash  payments  on  account  as  fol- 
lows :  Mar.  15,  $400.80;  Mar.  23,  $360.90.  On  Mar.  2T 
he  also  returned  goods  for  credit  amounting  to  $18.60.  Render 
a  statement  of  F.  E.  Smith's  account. 

2.  During  April  the  above  account  was  charged  for  merchan- 
dise as  follows:  Apr.  15,  $720.50;  Apr.  27,  $260.90.  The 
account  was  also  credited  for  cash  as  follows  :  Apr.  16,  $200.70  ; 
Apr.  28,  $100.00.     Render  the  April  statement. 

.  3.    Copy  and  find  the  balance  of  the  following  statement: 

Boston,  Mass.,  Feb.  1,  19 
Mks.  C.  M.  Shermak 

931  Beacon  St.,  City 
In  account  with  Spencer,  Mead  &  Co. 


Jan. 


1 

Account  rendered 

3 

2  pr.  Gloves 

2.50 

3  yd.  Velvet 

3.75 

12   "    Black  Silk 

2.10 

12 

6  pr.  Hose 

35^ 

2  Hats 

9.00 

30^  yd.  Muslin 

121;^ 

Cr. 

5 

2  pr.  Gloves 

2.50 

15 

IHat 

9.00 

13 


64 


BILLS  AND  ACCOUNTS 


181 


PAY   ROLLS 


PAY  ROLL 

For  the  week  end 

ing 

.^-^^4^' 

^ 

19 

Mo. 

NAME 

Number  oi  Houri'  Work  Euh  Day 

Toul  No. 
ofHotin 

w«« 

poHour 

.t^ 

REMARKS 

M 

T 

w 

T 

F 

s 

/ 

\(Z^^y//rr2/^^^^ 

<^ 

^ 

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f7 

r^f' 

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c 

'~(/7.  Co   A^^^y-rp—r^y'-T^ 

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This  form  is  most  common  among  manufacturing  establishments,  but 
it  is  also  used  by  printers,  contractors,  and  builders. 

Checks  are  sometimes  used  in  paying  off  employees,  but  most  large  con- 
cerns find  the  envelope  system  the  most  convenient  and  satisfactory.  To 
pay  off  employees  by  the  envelope  system  it  is  necessary  for  the  bookkeeper 
to  find  first  the  amount  of  money  required  and  then  the  bills  and  fractional 
currency  that  are  necessary  to  pay  each  employee.  The  amount  required  is 
the  total  of  the  pay  roll,  and  the  bills  and  fractional  currency  desired  may  be 
found  as  shown  in  the  following  illustration.  This  illustration,  called  a 
change  memorandum,  shows  the  method  of  finding  just  the  denominations 
wanted  for  the  pay  roll  at  the  top  of  the  page.  A  change  memorandum 
may  be  proved  correct  as  shown  in  the  pay-roll  memorandum  at  the  top  of 
page  182. 


No. 

Bills 

Coins 

$20 

$10 

$5 

$2 

$1 

50^ 

25  j^ 

10  J* 

hf 

\f 

1 
2 
3 
4 
5 
6 
7 
8 
9 
10 

1 

1 

1 
1 

1 

1 

1 
1 

1 

1 

1 

2 

1 

1 
1 

1 
1 

1 

1 
1 

1 

1 
1 

1 

1 
1 

1 
1 

1 

2 

2 

1 

1 
1 
1 

1 
1 

3 

4 

2 

2 

4 

7 

6 

6 

5 

6 

5 

9 

182 


PEACTICAL   BUSINESS  ARITHMETIC 


When  the  amount  of  the  pay  roll 
and  the  necessary  bills  and  frac- 
tional currency  have  been  deter- 
mined, a  check  payable  to  the  order 
of  Pay  Roll  is  written,  A  pay-roll 
memorandum  similar  to  the  accom- 
panying form  is  then  attached  to 
the  check  and  both  are  sent  to  the 
bank.  The  pay-roll  memorandum 
should  foot  the  same  as  the  pay-roll 
book,  and  is  therefore  a  check  upon 
the  correctness  of  the  change  memo- 
randum. 

In  a  large  pay  roll  the  adept 
bookkeeper  frequently  estimates  the 
kind  of  change  required.  This  is 
done  by  scanning  the  pay  roll  first 
to  find  the  number  of  pennies  re- 
quired, then  the  number  of  nickels, 
etc.     The  experienced  book-keeper  can 


FIRST  NATIONAL  BANK 

Westfield,  Mass. 

PAT-ROLL  MEMORANDUM 

NELSON  y  CO. 

require  the  following: 


make  a  very  accurate  estimate. 


PAY  ROLL    For  the  week  ending /trn/^ C^, 


Bills  and  silver  necessary 


50c  iSc  I Oc   5c 


id£ 


£JiL^ 


£2.2S3. 


Zo 


^ 


l£. 


sa: 


^ 


Jj^3Si 


LL 


Z£i 


n£/£^ 


z4 


JlSL'Ji^ 


£LiJJ 


^: 


A/^ 


^22j 


L2. 


"7 


J- 


7   C  7  ^/^ 


4^  igo  JJ^_Ji.,J'  JJi./iiJf/_lJf/i./''i/fSl 


WRITTEN   EXERCISE 


1.  Study  the  model  pay  roll,  page  181,  and  find  the  amount  of 
it  at  the  following  wages  per  hour  :  #1, 18^;  #2,  21|^;  #3,  25^; 
#4,  35^;  #5,  331^;  #6,  35^;  #7,  371^;  #8,  35)^;  #9,  271^; 
#10,  18|^.     Make  a  change  memorandum. 


BILLS  AND  ACCOUNTS 


183 


2.  Study  the  model  pay  roll  on  page  182,  and  then  find  the 
amount  of  it  at  the  following  wages  per  hour:  #1,  50^;  #2,  45^; 
#3,  831^;  #4,  35^;  #5,  27^^;  #6,  371^;  #7,  25^;  #8,  331^;  #9, 
44^^;  #10,  22f  ^;  #11,  22|^;  #12,  14f  ^;  #13, 121^;  #14,  30^. 

3.  Make  a  pay  roll  memorandum  from  problem  2. 

WRITTEN    REVIEW    EXERCISE 

1.    Find  the  amount  of  each  of  the  following  bills : 

New    Tork^  May  31,   ig 
AfESSRS.  Gray,  Salisbury  &  Co. 

Kochester,  N.Y. 

Bought  of  J,  E.  Page,  Sons  &  Co, 

Terms :  net,  60  da. ;   2%  10  da. 


Case 

PlECKS 

Description  of  Articles 

Yns. 

Price 

Items 

Amount 

#364 

10 

Velvieteen 
421   40    40    46    38i 
40    42     42     41     39 

25i? 

#359 

12 

Corduroy 

36  381   392  42     412  392 

37  37     41     45    41     40i 

66|i^ 

#371 
#360 

15 

0 

Gray  Homespun 

39  38     35    42    41 
45    39    41     34    37 
41     40     41     38    423 

Storm  Serge 

40  421    43     42     39    42^ 

831^' 

#373 

24 

Fine  English  Serge 
42     38     42     42     402  42i 
40    39    40    41     401  43 

42  42     382  38    41     42 

43  44    41     40    371  37 

1.37^ 

#381 

24 

Groveland  Flannel 
32    40    39    42    41     45 
45    46    35    41     38    41 
37     42     43     40     37     42 
37     40     42     41     44    41 

33| 

184  PEACTICAL   BUSINESS  AEITHMETIC 

2.  Make  out  a  bill  for  the  following  order.  Bill  the  English 
breakfast  tea  at  41  ^ ;  Finest  oolong  tea  at  Q5^ ;  Young  Hyson 
tea  at  97|^;  Choice  Japan  tea  at  59^;  Orinda  kaughphy  at 
$1.90;  raw  Java  coffee  at  30^^;  gluten  flour  at  30^  a  carton 
and  $7.15  per  barrel.  Assume  that  half  a  chest  of  tea  weighs 
75  lb.,  and  a  mat  of  coffee  70  lb. 

E.  M.  BARBER  &  SON 

RETAIL  GROCERS 
Springfield,  Mass..         Aug .  13 ,  19 

S.  S.  Pierce  Company 

Boston,  Mass. 

Gentlemen: 

Please  ship  us  via  B.  &  A.  R.R.,  the  follow- 
ing goods: 

3  hf.  cht.  English  Breakfast  Tea 

3  "    "   Finest  Oolong  Tea 

5  **    "   Young  Hyson  Tea 

25  lb.  Choice  Japan  Tea 

5  5-lb.  cans  Orinda  Kaughphy 

7  mats  Raw  Java  Coffee 

5  hf.  bbl.  Gluten  Flour 

25  5-lb.  cartons  Gluten  Flour 

Respectfully  yours 

3.  Boston,  Mass.,  Apr.  16,  E.  O.  Burrill,  Philadelphia,  Pa., 
bought  of  Jones,  Talcott  &  Co.,  on  account,  30  da.,  25  Turk- 
ish rugs  41  X  7  at  110.25  ;  750  yd.  matting  at  55^  ;  225  yd.  lin- 
oleum at  271^ ;  25  Turkish  rugs  %\  x  12  at  121.75 ;  25  Persian 
rugs  6  x9at  ^12.25;  12  Persian  rugs  7  x  11  at  116.25;  10  rolls, 
each  containing  150  yards,  Brussels  carpeting  at  §2.25  ;  275  yd. 
Moquette  carpeting  at  $1.75.     Find  the  amount  of  the  bill. 


BILLS  AND   ACCOUNTS 


185 


TIME  SLIP 

TIME  SLIP 

Friday,    4/26,   19 

— 

Saturd 

[ay,    4/27,    19— 

IN 

OUT 

IN 

OUT 

IN 

OUT 

IN 

OUT 

1 

751 

1201 

1256 

502 

1 

753 

1200 

1258 

502 

2 

747 

1202 

1247 

503 

2 

757 

1204 

1259 

501 

3 

744 

1204 

1254 

504 

3 

753 

1200 

1256 

504 

4 

751 

1205 

1255 

501 

4 

755 

1202 

1254 

502 

5 

753 

1206 

1259 

505 

5 

749 

1201 

1257 

504 

6 

751 

1202 

1259 

503 

6 

828 

1203 

1255 

503 

7 

859 

1201 

1254 

502 

7 

755 

1202 

1253 

501 

8 

756 

1202 

1250 

501 

8 

857 

1201 

1254 

502 

9 

757 

1201 

1259 

502 

9 

758 

1202 

1258 

504 

The  above  slips  show  a  record  of  time  for  9  employees  for  2  da.  in  a 
large  printing  establishment.  The  records  are  made  by  a  large  mechani- 
cal timekeeper,  and  at  convenient  periods  are  copied  in  the  pay-roll  book. 
Fractions  are  recorded  to  the  nearest  i  of  an  hour.  The  above  record  is 
based  on  an  eight-hour  day,  from  8  to  12  a.m.,  and  1  to  5  p.m.  If  a  record 
is  made  before  the  hour  for  beginning  work,  either  in  the  morning  or  at 
noon,  it  is  not  counted  in  the  regular  time,  but  if  an  employee  is  late,  his 
record  for  time  begins  at  the  nearest  multiple  of  ten  after  the  record  is 
made.  For  instance,  if  an  employee  rang  in  at  8:42  a.m.,  his  time  for  thfe 
morning  would  begin  at  8:50.  In  the  above  slip  for  Friday,  Xo.  1  rang 
in  at  7:51  and  left  at  12:01 ;  he  rang  in  at  12:56  and  rang  out  at  5:02  ; 
time,  8  hr. 

4.  Copy  the  following  pay  roll,  enter  the  time  for  Friday  and 
Saturday  (from  the  above  slips),  find  the  amount  of  the  pay  roll ; 
make  a  change  memorandum  and  a  pay-roll  memorandum. 


PAY  ROLL 

For  the  Week  Ending 

April 

27,  19- 

No. 

Name 

Number  of  Hours' 
Work  Each  Day 

Total 
No.  OF 

Wagks 
per 

TOTAL 

Remarks 

M. 

T. 

w. 

T. 

F. 

s. 

Hours 

Hour 

1 

A.  B.  Comer 

8 

8 

8 

8 

55f)^ 

2 

W.  D.  Ball 

8 

8 

8 

8 

U^^ 

3 

A.  M.  Snow 

8 

8 

8 

8 

U^f 

4 

R.  0.  Mark 

8 

8 

8 

8 

SS^f 

5 

Miss  Mary  Cane 

8 

n 

8 

8 

331^ 

6 

Miss  Ellen  Kyle 

8 

n 

8 

8 

35  j? 

7 

D.  M.  Garson 

8 

.7* 

8 

8 

35^ 

8 

S.  D.  Lane 

8 

7* 

7* 

8 

25^ 

9 

Miss  Cora  Knapp 

8 

8 

7i 

8 

22f)^ 

186 


PKACTICAL   BUSINESS   ARITHMETIC 


EXPRE^SAGE   AND   FREIGHTAGE 


These  Express  rates  went  into  e 

iffect  Febri 

lary  1,  191 

4,  in  con- 

formity 

with  the  order  of  the  Interstate  Commerce  Commission : 

Between  New 

'  York 

Between  New  York 

Between  New  York 

ANE 

•  Chicago 

AND  New 

Orleans 

and  Denver 

1st  class     2d  class 

1st  class 

2d  class 

1st  class 

2d  class 

51b.  31/ 

31/ 

41/ 

41/ 

•  47/ 

47/ 

6 

33 

32 

46 

46 

53 

53 

7 

35 

32 

50 

48 

58 

57 

8 

38 

32 

54 

48 

64 

57 

9 

40 

32 

59 

48 

69 

57 

10 

42 

32 

63 

48 

75 

57 

15 

53 

40 

84 

63 

1.02 

77 

20 

64 

48 

1.06 

80 

1.30 

98 

25 

75 

57 

1.27 

96 

1.57 

1.18 

Between  Chicago 

Between  Chicago 

Between  Chicago 

AND  Boston 

AND  Galveston 

and  Portland,  Ore. 

1st  class     2d  class 

1st  class 

2d  class 

1st  class 

2d  class 

5  1b.  31/ 

31/ 

39/ 

39/ 

63/ 

63/ 

6 

34 

33 

43 

43 

72" 

72 

7 

36 

33 

47 

45 

81 

80 

8 

38 

33 

51 

45 

•     89 

80 

9 

41 

33 

55 

45 

98 

80 

10 

43 

33 

59 

'45 

1.06 

80 

15 

54 

41   • 

78 

59 

1.50 

1.13 

20 

Q6 

50 

98 

74 

1.93 

1.45 

25 

77 

58 

1.17 

88 

2.36 

1.77 

Under  the  new  system  the  country  is  divided  into  blocks,  each  block 
covering  a  certain  designated  territory,  and  fixed  rates  are  made  for  certain 
weights  and  distances,  not  as  under  the  old  system,  at  so  much  per  pound. 

The  tables  given  herewith  suggest  the  manner  in  which  charges  are 
made  for  given  amounts  to  certain  points. 

First-class  matter  includes  all  merchandise ;  second-class  matter  applies 
to  food  and  drink,  and  these  terms  are  elaborated  and  explained  in  the 
instructions  to  express  agents.  On  small  packages  the  difference  in  charges 
for  first-class  matter  or  second-class  matter  is  very  slight  (sometimes  the 
same),  but  for  large  packages  and  long  distances  the  difference  is  marked. 


BILLS   AND   ACCOUNTS 


187 


WRITTEN   EXERCISE 


1.    Find  the  total  cost  of  sending  the  following  packages : 


10  lb.  first  class  from  New  York  to  Chicago.       ^'.^  \ 

5  lb.  second  class  from  Chicago  to  Boston. 
15  lb.  first  class  from  Chicago  to  Galveston. 
20  lb.  second  class  from  New  York  to  Denver.         '     O. 
10  lb.  first  class  from  New  York  to  New  Orleans.  V 


t 


2.  Find  the  total  cost  of  sending  the  following  packages : 

15  lb.  first  class  from  Chicago  to  Galveston. 

25  lb.  second  class  from  Chicago  to  Portland,  Ore. 

7  lb.  second  class  from  Boston  to  Chicago. 

9  lb.  first  class  from  Chicago  to  New  York. 
10  lb.  first  class  from  Galveston  to  Chicago. 

3.  Find  the  amount  of  the  following  freight  bill : 


Date  of  W.  B.AUt^/^ig       W.  B.  No.  A^^yf  Albany,  N.Y.A^i^^-o^g 

To  The  Interstate  Transportation  Company,  Dr, 

For  Transportation  fromA^^v^^^^^^uo  U^^-^^-gi^^^-z^ 


Weight 


'/  /  /  i'^ 


ZJ-^ 


Advance  charges 
Received  pay  men, 


No.  CarJ/Z^jT 


Freight  Agent 


// 
/^ 


P  P 


Bulky  goods  are  generally  sent  by  freight.  The  articles  are  divided 
according  to  quantity  and  character,  into  different  classes,  and  are  subject 
to  different  rates.  All  railroads  follow  some  official  classification.  All 
official  classifications  divide  freight  into  six  different  classes. 

Such  bulky  articles  as  furniture,  uncased,  is  subject  to  a  classification 
called  double  Jirst-class.  There  is  so  much  unoccupied  space  that  the  first- 
class  rate  is  doubled. 


188 


PRACTICAL   BUSINESS  ARITHMETIC 


Such  freight  as  organs  and  pianos  in  cases,  furniture,  statuary,  etc.,  is 
generally  designated  as  first-class  matter.  Baled  hay,  iron,  etc.,  in  car  loads, 
is  generally  designated  as  fifth-class  matter.  Building  blocks,  brick,  etc.,  in 
car-load  lots,  is  generally  designated  as  sixth-class  matter.  First-claso  rates 
are  the  highest  and  sixth-class  rates  are  the  lowest  charged. 

Between  most  points,  shipments  weighing  less  than  100  lb.  are  charged 
as  100  lb.,  irrespective  of  weight. 

BOSTON   &  ALBANY  RAILROAD 

Local  Freight  Tariff  between 


BOSTON 

,  MASS. 

AND 

Stations 

Rate  per  100  Lb. 

Stations 

Rate  per  100  Lb. 

Classes 

Classes 

J^ 

1 

3 

3 

4 

5 

6 

1 

2 

3 

4 

5 

110 

6 

21 

So.  Framingham 

14^ 

12^ 

10^ 

8^ 

()f 

5f 

98 

Springfield .    . 

28^ 

24^ 

20^ 

15^' 

9f 

32 

Westboro      .     . 

16^ 

14^ 

11^ 

9^ 

(i^ 

5<? 

108 

Westfield    .    . 

29^ 

25)?^ 

20^ 

Wf 

12^ 

w 

44 

Worcester    .    . 

m 

15^ 

13^ 

10^ 

If 

6f 

146 

Athol.    .    .    . 

33^ 

28^ 

23f 

18^ 

130 

m 

G2 

IVebster  .    .     . 

22<p 

19^ 

15^ 

12^ 

9f 

7f 

150 

Pittsfield     .    . 

33/^ 

28^ 

23^ 

18^ 

130 

\\f 

83 

Palmer     .    .     . 

mf 

22^ 

m 

w 

w 

9f 

202 

Albany    .    .    . 

35^ 

30^ 

25^ 

W 

14^ 

12^ 

4.  Using  the  table,  find  the  amount  of  freight  to  charge  on 
27,500  lb.  sixth-class  matter,  from  Boston  to  Pittsfield. 

5.  Using  the  above  table,  find  the  amount  of  freight  to 
charge  on  27,290  lb.  sixth-class  matter  and  890  lb.  first-class 
matter  from  Boston  to  Albany ;  to  Westfield. 

6.  Using  the  above  table,  find  the  amount  of  freight  to 
charge  on  14,790  lb.  fifth-class  matter  and  2170  lb.  second-class 
matter  from  Boston  to  Palmer;  to  Worcester;  to  Pittsfield; 
to  Springfield. 

7.  Using  the  above  table,  find  the  amount  of  freight  to 
charge  on  75  lb.  first-class  matter,  125  lb.  second-class  matter, 
1250  lb.  third-class  matter,  7290  lb.  fourth-class  matter,  21,490 
lb.  fifth-class  matter,  and  64,640  lb.  sixth-class  matter  from 
Boston  to  South  Framingham  ;  to  Westboro ;  to  Webster  ;  to 
Springfield  ;  to  Athol ;  to  Albany. 


BILLS   AND   ACCOUKTS  189 


ORAL  REVIEW  EXERCISE 

Each  problem  on  pages  189  and  190  should  he  completed  in 
approximately  four  minutes.     Without  copying,  find  the  cost  of: 


1. 

2. 

< 

i. 

32 

yd. 

at  61/ 

176 

yd. 

at  121/ 

149 

yd. 

at  25/ 

240 

yd. 

at  $i.l2i 

177 

yd. 

at  50/ 

150 

yd. 

at  $  1.33i. 

25 

yd. 

at  S  2.50 

210 

yd. 

at  284/ 

•  120 

yd. 

at  $1.25 

19 

yd. 

at  41/ 

291 

yd. 

at  3.3|/ 

169 

yd. 

at  11/ 

57 

yd. 

at  66f  / 

104 

yd. 

at  21/ 

162 

yd. 

at  121/ 

36 

yd. 

at  3^/ 

98 

yd. 

at  7/ 

48 

yd. 

at6|/ 

241 

yd. 

at  8/ 

90 

yd. 

at6|/ 

33^ 

yd. 

at  9/ 

190 

yd. 

at  25/ 

45 

yd. 

atSL33l 

174 

yd. 

at  30/ 

75 

yd. 

at  28/ 

45 

yd.  at  45/ 

291 

yd.  at  3/ 

75 

yd. 

at  121/ 

706 

yd. 

at  331/ 

117 

yd. 

at  9/ 

42 

yd. 

at  21/ 

221 

yd. 

at  8/ 

18 

yd. 

at  81/ 

246 

yd. 

at  11/ 

146 

yd.  at  11/ 

1821 

yd. 

at  10/ 

48 

yd. 

at  101/ 

74 

yd. 

at  121  / 

179 

yd.  at  20/ 

28 

yd.  at  6/ 

78 

yd. 

at  25/ 

64 

yd. 

at  121/ 

144 

yd. 

at  12^/ 

44 

yd. 

at  SI. 25 

167 

yd.  at  50/ 

33 

yd. 

4. 

at  331/ 

48 

yd. 

5. 

at  $1.50 

688 

yd. 

at  $1.10 

96 

yd. 

at  371/ 

36 

yd. 

at  $1.25 

521 

yd. 

at  10/ 

129 

yd. 

at  11/ 

55 

yd. 

at  11/ 

156 

yd. 

at  25/ 

75 

yd. 

at  11/ 

143 

yd. 

at  50/ 

85 

yd. 

at  85/ 

75 

yd. 

at  75/ 

36 

yd.  at  70/ 

144 

yd. 

at  16f  / 

27 

yd. 

at  80/ 

55 

yd.  at  55/ 

34 

yd. 

at  90/ 

73 

yd. 

at  11/ 

95 

yd. 

at  30/ 

125 

yd. 

at  20/ 

^b 

yd. 

at  65/ 

112 

yd. 

at  142  / 

53 

yd. 

at  25/ 

94 

yd. 

at  331  / 

47 

yd. 

at  33I-/ 

29 

yd. 

at  66f  / 

63 

yd. 

at  111/ 

53 

yd. 

at  331/ 

99 

yd. 

at  25/ 

139 

yd. 

at  50/ 

17 

yd. 

at  66f  / 

88 

yd. 

at  371/ 

64 

yd. 

at  62^/ 

104 

yd. 

at  121/ 

176 

yd. 

at  121  / 

98 

yd. 

at  16f  / 

80 

yd. 

at6|/ 

25 

yd. 

at  25/ 

225 

yd.  at  25/ 

77 

yd. 

at  30/ 

88 

yd. 

at  9^5^/ 

67 

yd. 

at  331/ 

99 

yd.  at  40/ 

57 

yd.  at  50/ 

190  PEACTICAL   BUSIKESS   ARITHMETIC 


7. 

8. 

9- 

128  yd.  at  11/ 

219  yd.  at  11/ 

65  yd.  at  80/ 

73  yd.  at  60/ 

85  yd.  at  30/ 

83  yd.  at  40/ 

76  yd.  at  60/ 

94  yd.  at  25/ 

145  yd.  at  11/ 

177  yd.  at  11/ 

89  yd.  at  11/ 

63  yd.  at  11/ 

72  yd.  at  11/ 

28  yd.  at  2^/ 

151yd.  at  331/ 

270  yd.  at  Hi/ 

112  yd.  at  61/ 

49  yd.  at  75/ 

36  yd.  at  11/ 

191yd.  at  50/ 

124  yd.  at  $1.25 

185  yd.  at  25/ 

781  yd.  at  10/ 

180  yd.  at  121/ 

225  yd.  at  20/ 

306  yd.  at  331/ 

360  yd.  at  371/ 

39  yd.  at  S  1.331 

122  yd.  at  21/ 

24  yd.  at  $1,121 

49  yd.  at  66f/ 

32  yd.  atSi.75 

165  yd.  at  6|/ 

42  yd.  at  S  2.50 

92  yd.  at  121/ 

175  yd.  at  8/ 

25  yd.  at  S  1.10 

224  yd.  at  7/ 

171yd.  at  11/ 

22  yd.  at  6|-/ 

240  yd.  at  21/ 

132^  yd.  at  10/ 

125  yd.  at  36/ 

276  yd.  at  11/ 

,  110  yd.  at  25/ 

108  yd.  at  9/ 

68  yd.  at  8/ 

51yd.  at  121/ 

216  yd.  at  12-1/ 

125  yd.  at  12/ 

301yd.  at  25/ 

10. 

11. 

12. 

62  yd.  at  41/ 

144  yd.  at  871/ 

97  yd.  at  30/ 

189  yd.  at  111/ 

25  yd.  at  S  1.62 

36  yd.  at  $1.16f 

78  yd.  at  40/ 

14  yd.  atS1.14f 

225  yd.  at  8/ 

334  yd.  at  7/ 

512  yd.  at  6/ 

1431  yd.  at  4/ 

255  yd.  at  5/ 

1171yd.  at  10/ 

55  yd.  at  101/ 

78  yd.  at  11/ 

45  yd.  at  11/ 

15  yd.  at  If/ 

118  yd.  at  11/ 

155  yd.  at  12/ 

235  yd.  at  20/ 

187  yd.  at  25/ 

247  yd.  at  50/ 

56  yd.  at  331/ 

88  yd.  at  331/ 

92  yd.  atl2J/ 

48  yd.  at  121/ 

96  yd.  at  371/ 

55  yd.  at  16f/ 

84  yd.  at  121/ 

:05i  yd.  at  10/ 

37  yd.  at  101/ 

165  yd.  at  25/ 

232  yd.  at  11/ 

42  yd.  at  SI. 25 

192  yd.  at  121/ 

36  yd.  at  S  1.331- 

24  yd.  at$1.66f 

145  yd.  at  5/ 

256  yd.  at  6/ 

178  yd.  at  7/ 

231yd.  at  8/ 

143  yd.  at  9/ 

321yd.  at  11/ 

148  yd.  at  16f  / 

64  yd.  at  $1.25 

24  yd.  at  S  1.871 

121yd.  at  25/ 

51yd.  at  S  1.331- 

36  yd.  atS1.66| 

1101  yd.  at  10/ 

a. 

16 

/. 

150 

h. 

24  yr. 

0- 

21yd. 

e. 

64  hr. 

h. 

65   A. 

d. 

12  men 

i. 

17  books 

e. 

15  desks 

J- 

34  houses 

DENOMINATE   NUMBERS 
CHAPTER   XV 

DENOMINATE  QUANTITIES 
EEVIEW   OF  THE   COMMON   TABLES^ 

ORAL  EXERCISE 

1.  Which  of  the  following  numbers  are  concrete  ?  which  are 
abstract?  which  are  denominate? 

k.  36  min. 

I.  5  yd.  2  ft. 

m,  3  yr.  4  mo. 

n.  10  T.  75  lb. 

0.  5  A.  61  sq.  rd. 

2.  Define  an  abstract  number;  a  concrete  number;  a  de- 
nominate number;  a  simple  number ;   a  compound  number. 

3.  Which  of  the  numbers  in  question  1  are  simple  ?  which 
are  compound  ? 

ORAL   EXERCISE 

1.    Repeat  the  table  of  avoirdupois  weight. 
•   2.    Repeat  the   table    of   long    measure;  of   surveyors'   long 
measure;  of  square  measure  ;  of  surveyors'  square  measure. 

3.  Repeat  the  table  of  cubic  measure;  of  dry  measure;  of 
liquid  measure;  of  time  ;  of  angular  measure;  of  United  States 
money  ;  of  English  -money. 

4.  Name  a  number  expressing  distance ;  two  numbers  ex- 
pressing area  ;  two  expressing  value  ;  three  expressing  capacity. 

5.  How  many  statute  miles  in  a  degree  of  the  earth's  sur- 
face at  the  equator  ?  how  many  geographical  miles  ?  How 
many  feet  in  a  statute  mile  ?  how  many  inches  ? 

1  Tables  of  weights  and  measures  may  be  found  in  the  Appendix  B. 

191 


192  PKACTICAL   BUSINESS   ARITHMETIC 

EEDUCTION 

ORAL   EXERCISE 

1.  Change  42  ft.  to  inches ;   to  yards. 

2.  Express  15  yd.  as  feet ;   as  inches. 

3.  Reduce  80  qt.  to  gallons ;  to  pints. 

4.  Change  128  qt.  to  pecks  ;  to  bushels. 

5.  Express  120  pt.  as  quarts ;  as  gallons. 

6.  What  part  of  a  yard  is  2  ft.?  J  ft.?  ^  ft.? 

7.  Reduce  5  bu.  to  pecks ;  to  quarts  ;  to  pints. 

Reduction   Descending 
206.   Example.     Reduce  4  T.  75  lb.  to  ounces. 

Solution.     Since  1  T.  =  2000   lb.,    4    T.  =  4  times         2000 
2000  lb.  =  8000  lb.;  and  with  the   75   lb.   added  this  =  4 

8075  lb.     Since  1  lb.  =  16  oz.,  8075  lb.  =  8075  times  16  oz. 
=  129,200  oz.,  the  required  result. 

8075  times  16  oz.  =  16  times  8075  oz.;  therefore  8075 


8075 
16 


times  16  oz.  is  found  as  shown  in  the  margin.  HjU^UU,  JNo.  01  OZ. 

WRITTEN   EXERCISE 

Reduce : 

1.  115'  6''  to  inches.  5.  SJ  rd.  to  feet. 

2.  12  bu.  4  qt.  to  pecks.  6.  IJ  T.  to  ounces. 

3.  £  16  15s.  to  shillings.  7.  12  A.  to  square  feet. 

4.  211  rd.  3  ft.  to  inches.  8.  161  cd.  to  cubic  feet. 

ORAL  EXERCISE 

1.  How  many  pecks  in  \  bu.?  in  J  bu.? 

2.  Change  .25  A.  to  square  rods;  .375  A.;  75  A. 

3.  Reduce  J  gal.  to  pints.     Express  J  rd.  as  inches;  as  yards. 

WRITTEN   EXERCISE 

Reduce : 

1.  I  mi.  to  feet.  4.  |  yd.  to  inches. 

2.  .75  cd.  to  cubic  feet.  5.  .375  mi.  to  feet. 

3.  ^ef  A.  to  square  feet.  6.  r^^  hr.  to  seconds. 


DENOMINATE   QUANTITIES  193 

Reduction  Ascending 

207.    Example.     Express  176  qt.  dry  measure  in  higher  de- 
nominations. iTP       Q       oo  oo    1 

176  -r-  8  =  22,  or  22  pk. 
Solution.    Since  8  qt.  =  1  pk.,  divide  by  8        99   .   j_  __  n;         i 
and  obtain  as  a  result  22  pk.  Since4pk.  =  lbu.,  *        ~ 

divide  by  4  and  obtain  as  a  result  5  bu.  2  pk.  mamder  01  ^, 

or  5  bu.  2  pk. 

WRITTEN   EXERCISE 
Reduce  to  Jiigher  denominations : 

1.  3840  ft.                   5.    816  pk.  9.  15,120'' 

2.  1054  pt.                   6.    106,590  ft.  10.  51,200  cu.  ft. 

3.  14,400  sec.               7.   43,560  sq.  in.  11.  145,152  cu.  in. 

4.  2000  sq.  in.             8.    27,900  lb.  avoir.  12.  27,900  oz.  avoir. 

ORAL  EXERCISE 

1.  Reduce  ^  ft.  to  the  fraction  of  a  yard. 

2.  Change  .16  cwt.  to  the  decimal  of  a  ton. 

3.  What  part  of  a  yard  is  1  in.?  2  in.?  J  in.? 

4.  What  decimal  part  of  an  acre  is  16  rd.?  40  rd.? 

5.  What  part  of  35  bu.  is  7  bu.?  of  1 J  bu.  is  J  bu.? 

WRITTEN   EXERCISE 

1.  Reduce  1|^  in.  to  the  fraction  of  a  foot;  of  a  yard. 

2.  Reduce  10s.  9d.  to  the  fraction  of  a  pound  sterling. 
Solution.     There  are  12d.  in  a  shilling  and  20s.     lOs.  and9c?.  =  1296?. 

in  a  pound  sterling,  or  240d.  £1=  ^4:0d 

To  find  what  fractional  part  of  a  pound  sterling  -  cotc 

10s.  and  M.  are,  use  the  following  statement :  210"  ~  *  ' 

10s.  9d.  =  129d.    £l  =  240(i.  Therefore,  10s.  9c?.  =  or  ^.5375 

^|§  of  a  £,  or  £.5375. 

3.  Reduce  4  yd.  1|  ft.  to  the  decimal  of  a  rod. 

4.  Reduce  10s.  6d.  2  far.  to  the  decimal  of  a  pound  sterling. 

5.  Reduce  5  T.  721  lb.  to  tons  and  decimal  of  a  ton ;  6  T. 
1750  lb.;   12  T.  290  lb.;  29,240  lb.;  28,390  lb. 

6.  Find  the  cost  of  1750  lb.  of  coal  at  16.25  per  ton;  of 
2170  lb.;  of  690  lb.;  of  1360  lb.;  of  3240  lb.;  of  32590  lb. 


194  PRACTICAL   BUSINESS  AEITHMETIC 

ADDITION   AND   SUBTRACTION 

ORAL  EXERCISE 

State  the  sum  of : 


1. 

12  ft.  1  in. 
6        3 

2. 

5  lb.  8  oz. 

6  3 

6. 

11  ft.  2  in. 

8        1 
3        3 

rence  between: 
2. 

75  rd.  121  ft. 
26           41 

6. 

12  mo.  31  da. 
8          17 

3. 

15  rd.  5  ft. 
17        2 

7. 

5  bu.  1  pk. 

8  0 

9  1 

3. 

30  yd.  2  ft. 

n      11- 

7. 

11  mo.  15  da. 

2            9 

4. 

10  mi.  8  rd. 
8       40 

5. 

5  rd.  2  ft. 

8         21 
7         21 

8. 

5  mi.  20  rd. 
17         13 
11         10 

State  the  diffe 

1. 

90  mi.  300  rd. 

75         120 

4. 

44  bu.  3  pk. 

29         1 

5. 

11  mo.  12  da. 

6            6 

8. 

98  gal.  2  qt. 
69          1 

208.    Examples.     1.    Three  jars  of  butter  weighed  48  lb.  7  oz., 
45  lb.  9  oz.,  and  53  lb.  11  oz.     Find  the  total  weight. 

Solution.     Arrange  the  numbers  as  in  simple  addition,  .^  ,,  _ 

so  tliat  units  of  the  same  order  stand  in  the  same  vertical  .  >  A 

column.      Adding  the  first  column  at  the  right,  the  result  is         ^^  /: 

27  oz.  =  1  lb.  11  oz. ;  write  11  oz.  and  carry  1  lb.      Adding        "^"^  ^^ 

the  pounds,  the  sum  is  147.  .  147  lb.  11  OZ. 

2.    From  a  barrel  containing  379  gal.  1  qt.   of  molasses,  17 
gal.  3  qt.  were  sold.     How  much  remained  unsold  ? 

Solution.     Arrange  the  numbers  as  in  simple  subtraction,      07  ^.^    lot 
so  that  units  of  the  same  order  stand  in  the  same  vertical      17         *  ^ 
column.     3  qt.  cannot  be  subtracted  from  1  qt.;   therefore 


mentally  take  1  gal.  (4  qt.)  from  37  gal.  and  add  it  to  1  qt.,  ^^  ^^^'  ^  ^^' 
making  5  qt.  5  qt.  —  3  qt.  =  2  qt.  Inasmuch  as  1  gal.  was  added  to  1  qt.,  there 
are  but  36  gal.  remaining  in  the  minuend  ;  36  gal.  —  17  gal.  =  19  gal. 


DENOMIISrATE  QUANTITIES  195 


WRITTEN   EXERCISE 


Find  the  sum  of  : 

1. 

2. 

3. 

4 

L 

£140  68. 

£139   5s. 

84  T 

.  75  lb. 

279  T 

.  840  lb. 

159  3 

214   5 

96 

14 

364 

210 

162  4 

921   3 

78 

79 

872 

220 

139  2 

141    7 

37 

41 

146 

140 

167  4 

10   9 

19 

63 

214 

180 

129  3 

171    8 

84 

79 

926 

230 

136  4 

215   7 

97 

13 

210 

420 

147  2 

321   5 

87 

125 

75 

750 

Find  the  diffi 

3rence  between : 

5. 

6. 

7. 

8. 

11  mo.  17  da. 

11  mo.  1  da. 

8 

mo.  14  da. 

9  mo.  17  da. 

8         31 

9       31 

2 

29 

2 

31 

9.    From  a  pile  of  wood  containing  74|  cd.,  28^  cd.  and  15^ 
cd.  were  sold.     How  much  remained  unsold? 

10.  I  owned  a  farm  of  340  A.  when  I  bought  an  adjoining 
field  of  741  A.  I  then  sold  140f  A.  What  is  the  remainder 
of  the  farm  worth  at  175  per  acre  ? 

11.  An  English  merchant  had  on  hand  Jan.  1  goods  valued 
at  X5927  10s.;  during  the  following  six  months  he  bought 
goods  at  a  cost  of  <£  4920  10s.  and  sold  goods  to  the  amount  of 
£  7926  4s.  If  the  value  of  the  goods  on  hand  July  1  of  the 
same  year  Avas  £4120  10s.,  what  has  been  the  gain  or  loss  in 
English  money  ?  in  United  States  money  ? 

Finding  the  Difference  between  Dates 

209.  In  the  foregoing  problems  in  addition  and  subtraction 
only  compound  numbers  of  two  denominations  were  used. 
These  are  practically  the  only  compound  numbers  met  with  in 
business,  if  the  case  of  finding  the  difference  between  two  dates 
is  excepted. 


196  PRACTICAL   BUSINESS   ARITHMETIC 

210.  The  difference  between  two  dates  may  be  found  by  com- 
pound, subtraction,  or  by  counting  the  actual  number  of  days 
from  the  given  to  the  required  date. 

In  business  transactions  involving  long  periods  of  time,  the  difference  is 
generally  found  by  compound  subtraction  ;  but  in  transactions  involving 
short  periods  of  time,  the  difference  is  generally  found  by  counting  the 
exact  number  of  days. 

211.  Examples,  i.  A  mortgage  dated  Oct.  15,  1915,  was 
paid  Apr.  6,  1921.     How  long  had  it  run  ? 

Solution.  Write  the  later  date  as  the  minu-  1921  yr.  4  mo.  6  da, 
end  and  the  earlier  date  as  the  subtrahend.  April      1915  IQ  15 

being  the  4th  and  October  the  10th  month,  write  r  7  K^     t 

4  and  10  respectively  instead  of  the  names  of  the  J    •     ' 

months.     Consider  30  da.  a  month  and  12  mo.  a  year  and  subtract  as  usual. 

2.    Find  the  difference  between  Apr.  21  and  July  27. 

Solution.     Write  the  number  of        9  J^^  [^i  April 
days  remaining  in  April,  the  number      g|  ^.^    ^^  Mav 
in   May  and  June,  and  finally  the      qq  j^,    :y.  June 
number  in  July  up  to  and  including      97  ^o     \r^   Inl  v 

July  27.     The  sum  of  these  numbers      7_    ,       .  ";       -i    r»-«   ^      t   i      n^ 

is  the  required  time  expressed  with      '^^  '^^'  ^^^m  April  21  to  July  27 
exactness.     Observe  that  the  total  time  excludes  the  first  and  includes  the  last 
day  of  the  given  dates. 

ORAL   EXERCISE 

State  the  exact  number  of  days  between  : 

1.  Mar.  12  and  Apr.  16.  5.  July  1  and  Oct.  1. 

2.  Apr.  27  and  May  31.  6.  June  30  and  Sept.  1. 

3.  May  31  and  July  18.  7.  July  31  and  Nov.  7. 

4.  June  7  and  Aug.  16.  8.  Aug.  31  and  Dec.  1. 

WRITTEN   EXERCISE 
Find  the  exact  number  of  days  between : 

1.  Apr.  2  and  Nov.  25.  5.    Mar.  18  and  Nov.  27. 

2.  Mar.  1  and  Sept.  18.  6.    Mar.  17  and  July  28. 

3.  Mar.  15  and  Nov.  2.  7.    June  16  and  Sept.  18. 

4.  Apr.  21  and  Dec.  31.  8.    June  19  and  Nov.  29. 
9.    Find  the  difference  between  Jan.  3,  1915,  and  each  of  the 

following  dates:   May  15,  1912;  Sept.  6,  1913;    Apr.  8,  1909; 
Mar.  12,  1897.     Find  the  difference  by  compound  subtraction. 


DENOMINATE   QUANTITIES  197 

MULTIPLICATION    AND   DIVISION 
ORAL  EXERCISE 
Multiply :  Divide : 

1.  3  ft.  by  6.  7.    27  yd.  by  9. 

2.  IJ  mi.  by  8.  8.    225  ft.  by  TJ  ft. 

3.  9  lb.  4  oz.  by  2.  9.   48  ft.  6  in.  by  2. 

4.  18  lb.  1  oz.  by  9.  lO.   540  yd.  by  18  yd. 

5.  17  yd.  2  in.  by  9.  ii.   164  lb.  12  oz  by  4. 

6.  19  gal.  1  qt.  by  3.  12.    640  mi.  160  rd.  by  20. 
212.    Examples,     l.    How  much  hay  in  8  stacks  each  contain- 
ing 5  T.  760  lb.  ? 

Solution.     8  times  760  lb.  =  6080  lb.  =  3  T.  80  lb.  ;         5  ^     ^qq  u^ 
"write  80  in  place  of  pounds  and  carry  3.     8  times  5  T.  = 
40  T. ;  40  T.  +  3  T.  carried  =  43  T.    The  required  result  ^ 


is  therefore  43  T.  80  lb.  43  T.      80  lb. 

2.  An   importer   paid  <£  87  10s.  for   50  pc.  of   bric-a-brac. 
What  was  the  cost  per  piece  ? 

Solution.     Since  50  pc.   cost  £87  10s.,  1  pc.  costs  £     1      15s. 

3*0  of  £  87  10s.     -^^  of  £  87  =  £  1  with  an  undivided  re-  ^0T£~R7 TO — ' 

mainder  of  £  37  ;   write  £  1  in  the  quotient  and  add  ^ 

£  37  to  the  next  lower  denomination  ;  £  37  10s.  =  750s.  ^^  of   750s.  =  15s. 

3.  At  10s.  6d.  per  yard,  how  many  yards  can  be  bought  for 
£  15  15s.  ? 

Solution.     The  dividend  and 
divisor   are     concrete    numbers ; 

therefore     reduce    them    to    the  <£  15  15s.  =  3780a. 

same  denomination  before  divid-  10s.  Qd.      =  126c?. 

ing.     £15  15s.  =  3780d,  10s.  6cl  gygQ,^.  ^  126c^.  =  30,  no.    of  yd. 

=  126d      87S0d.   -r-  126(7.  =  30 ;  'J' 

that  is  30  yd.  can  be  bought. 

ORAL  EXERCISE 

1.  At  72  ^  per  gross  what  will  2  doz.  buttons  cost  ?  4  doz.  ? 
7  doz.  ? 

2.  How  many  3-oz.  packages  can  be  put  up  from  4  lb.  of 
pepper  ? 

3.  Find  the  cost  of  3  T.  of  bran  at  30^  per  hundredweight; 
of  5  T.  at  50^  per  hundredweight. 


198  PRACTICAL   BUSINESS  ARITHMETIC 

4.  How  many  1-lb.  packages  can  be  put  up  from  15  T.  of 
breakfast  food  ? 

5.  When  coal  is  $  6  per  ton  what  will  7000  lb.  cost  ?  6400 
lb.?  3600  lb.? 

6.  Find  the  cost  of  2400  lb.  of  flour  at  1 2.25  per  hundred- 
weight; of  4400  lb.;  of  3200  lb. 

7.  At  12|  ^  per  quire  what  will  480  sheets  of  paper  cost  ? 
240  sheets  ?  2880  sheets  ?  720  sheets  ? 

8.  I  buy  3  qt.  of  milk  per  day.  If  I  pay  8  ^  per  quart, 
what  is  my  bill  for  July  and  August  ? 

9.  I  bought  3  gro.  pens  at  60  p  a  gross  and  sold  them  at  the 
rate  of  2  for  1  ^  ;  what  was  my  gain  or  loss  ? 

10.  I  bought  Z\  bu.  of  apples  at  %  1.00  per  bu.  and   sold 
them  at  50  ^  a  peck.     What  was  my  gain  ? 

11.  I  sold  4 J  cd.  of  wood  for  %  27  and  thereby  lost  $  9  on 
the  cost.     What  was  the  cost  per  cord  ? 

WRITTEN  EXERCISE 

1.  Find  the  cost  of  10  pwt.  7  gr.  of  old  gold  at  11.25  per 
pennyweight;   of  12  pwt.  4  gr.  at  $1.10  per  pennyweight. 

2.  I  bought  3|-  A.  of  city  land  at  $125  an  acre  and  sold  it 
at  50  ^  per  square  foot.     Did  I  gain  or  lose  and  how  much  ? 

3.  Give  the  length  of  a  double-track  railroad  that  can  be 
laid  with  352,000  rails  30  ft.  long. 

4.  I  bought  a  barrel  of  cranberries  containing  2\  bu.  at  $4 
per  bushel  and  retailed  them  at  15^  a  quart.  Did  I  gain  or 
lose  and  how  much  ? 

5.  From  a  farm  of  375  A.  I  sold  25|  A.  What  is  the  re- 
mainder worth  at  $125  per  acre  ? 

6.  Find  the  cost  (a)  in  English  money  and  (5)  in  United 
States  money  of  360  doz.  cotton  hose  at  b%.  2d. 

Solution,     (a)  5s.  2d.  =  5|s.      360  times  5is.  =  1860s.  =  £  93,  the  cost  in 
English  money. 
(6)  £1  =.$4.8665.       93   times  $4.8665  =  $452.58,  the  cost   in 
United  Btates  money. 


DENOMINATE   QUANTITIES  199 

7.   Copy  and  find  the  amount  of  the  following  invoice : 


Tgrmg      yZj'^^-Y^  ii/^sl^ 


Bought  of  E.  M.  LLOYD  &  SON 


^ 


^z. 


/.r^  a^^--/^.^^^J'€:^^Y?^y^ 


z^r^ 


:;^S^^^Y^^^^^'^!^^r^^-^^->t,    ^/j 


-^Tf^^k 


7^^.^^  ^^^^ 


5^ 


^k 


jkjutm. 


5/2,  4/3,  and  12/-  in  the  price  column  =  55.  2c?.,  45.  M.,  and  12s., 
respectively. 

8.  Reduce  $2500  to  English  money. 

Solution.     $2500  -  $4.8665  =r  513.72,    or    £513.72.       .72  x  20s.  =  14.4s. 
.4  X  12d.  r=  4.8d.     .8  X  4  far.  =  3.2  far.     Hence  $2500  =  £513  14s.  4(Z.  3.2  far. 

9.  Find  the  value  in  United  States  money  of  a  post-office 
money  order  for  X5  18s.  6<i. ;   for  <£3  12s. 

10.    Without  copying,  find  the  amount  of  the  following  invoice : 


L&iht  Scotland,. 


^^/  /  ^f 


.19. 


INVOICE    OF  HOSIERY 


Z^tZ^L^^    In  the  ;iipnm!!.h\pLyCA^^^j>W^ 


u^^y 


c^?-^?y. 


^^. 


200 


PRACTICAL   BUSINESS  ARITHMETIC 


11.  A  druggist  bought  by  avoirdupois  weight  5  lb.  of  pep- 
permint oil  at  $  2.50  per  pound  and  retailed  it  at  50  ^  an 
ounce,  apothecaries'  weight.     What  was  his  gain  ? 

213.  Farm  products  which  are  handled  in  bulk  are  frequently 
bought  and  sold  by  the  bushel.  The  statutory  weights  of  the 
bushel  for  some  of  the  common  commodities  are  shown  in  the 
following  table : 

Statutory  Weights  of  the  Bushel 


Commodities 

Weight  in 

AVOIRDITHOIS 

Poinds 

Exceptions 

Barley- 

48 

Ala.,  Ga.,  Ky.,  and  Penn.,  47;  Ariz.,  45;  Cal.,  50. 

Beans 

60 

N.  H.  and  Vt.,  62. 

Clover  Seed 

60 

Corn,  Shelled 

56 

Ariz.,  54;  Cal.  52. 

Oats 

32 

Me.,N.J.,  Va.,30;  Md.,26. 

Potatoes,  Irish 

60 

Md.,  Penn.,  and  Va.,  56. 

Rye 

56 

Cal.,  54. 

Wheat 

60 

214.     Example.     What  will  4260  lb.  of  wheat    cost  at  80  J^ 
per  bushel? 

Solution.    In  examples  of  this   character   the  71 

principles  of  cancellation  may  be  applied  to  advan-      ^200  X  80^  =  ^  56  80 
tage.  ^0 

In  problems  1-4  in  the  following  exercise  the  price  is  per  bushel  in  each  case. 

WRITTEN   EXERCISE 

1.  Find  the  total  value  of : 
66401b.  wheat  at  84^. 
42301b.  wheat  at  95^. 

2.  Find  the  total  value  of : 
32641b.  oats  at  25^. 
24001b.  oats  at  48^. 
25601b.  oats  at  37^^. 

3.  Find  the  total  value  of : 
3660  lb.  clover  seed  at  14.50. 
1200  lb.  clover  seed  at  14.75. 
2472  lb.  clover  seed  at  $4.20. 


12601b.  wheat  at  90^. 
61201b.  wheat  at  871)^. 


69511b.  oats  at  32^. 
19201b.  oats  at  331^. 
3840  lb.  oats  at  29J^. 


5040  lb.  shelled  corn  at  47^^. 
2800  lb.  shelled  corn  at  56  j^. 
2240  lb.  shelled  corn  at  73^. 


CHAPTER   XVI 


PRACTICAL    MEASUREMENTS 
DISTANCES   AND   SURFACES 

Distances 

215.  An  angle  is  the  divergence  of  two  lines  from  a  common 
^^^^A    point. 

B^^— C  Thus  the  divergence  of  the  lines  BA  and  BC  from 

the  point  B  is  the  angle  ABC. 

216.  A  right  angle  is  the  angle  formed  when  one  straight  line 
so  meets  another  as  to  make  the  two  adjacent 
angles  equal.     The  lines  forming  the  angles  are 
perpendicular  to  each  other.  c- 

Thus  the  two  angles  ABC  and  ABD  are  right  angles,  and  the  lines  AB 
and  CD  are  perpendicular  to  each  other. 

217.  An  acute  angle  is  less  than  a  right  angle  ;  an  obtuse 
^  angle  is  greater  than  a  right  angle. 

__\^ Thus  the  angle  ABC  is  an  acute  angle,  and  the  angle 

^  ABD  is  an  obtuse  angle. 

218.  A  surface  is  that  which 
has  length  and  width,  but  not 
measurable  thickness.  A  level 
surface,  as  the  surface  of  still 
water,  is  called  a  plane  surface 
or  a  plane. 

219.  A  rectangle  is  a  plane  figure  bounded  by  four  straight 
lines  and  having  four  right  angles. 

A  square  is  a  rectangle  whose  sides 
are  all  equal. 

201 


■^^^'4^ 


202 


PRACTICAL   BUSINESS  ARITHMETIC 


220.  A  triangle  is  a  plane  figure  bounded  by  three  straight 
lines  and  having  three  angles. 

A  triangle  is  called  equilateral  when  all  its  sides  are  equal ; 
isosceles  when  any  two  of  its  sides  are  equal;  scalene  when  no 
two  of  its  sides  are  equal. 

221.  A  right-angled  triangle  is  a  triangle  having  a  right 
angle. 

A  triangle  containing  an  acute  angle  is  sometimes  called  an 
acute-angled  triangle ;  a  triangle  containing  an  obtuse  angle,  an 
obtuse-angled  triangle. 

222.  The  perimeter  of  a  plane  figure  is  the  distance  around  it. 

223.  A  circle  is  a  plane  figure  bounded 
by  a  regularly  curved  line,  every  point  of 
which  is  equally  distant  from  a  point  within 
called  the  center.  The  circumference  of  a 
circle  is  the  curved  line  which  bounds  it ; 
the  diameter  is  any  straight  line  passing 
through  the  center  and  terminating  in  the 
circumference ;  the  radius  is  one  half  the 
diameter.     An  arc  is  any  part  of  the  circumference  of  a  circle. 

224.  It  is  proved  in  geometry  that  the  circumference  of  a 
circle  is  3.1416  times  the  diameter. 

225.  Therefore,  to  find  the  circumference  of  a  circle  when 
the  diameter  is  given,  multiply  the  diameter  hy  3.1416. 

226.  And,  conversely,  to  find  the  diameter  of  a  circle  when 
the  circumference  is  given,  divide  the  circumference  by  3.1416. 

WRITTEN  EXERCISE 

1.  Draw  neat  figures  to  represent  each  of  the  following: 
rectangle,  triangle,  square,  circle,  right-angled  triangle,  equi- 
lateral triangle,  isosceles  triangle,  scalene  triangle,  radius  of  a 
circle,  arc  of  a  circle. 

2.  A  parlor  is  18  ft.  6  in.  long  and  12  ft.  3  in.  wide. 
What  will  be  the  cost,  at  28^  per  foot,  of  a  molding  extend- 
ing around  the  room  ? 


PRACTICAL   MEASUREMENTS 


203 


Trd: 


3.  The  circumference  of  a  circle  is  113.0976  ft.  What  is  the 
length  of  the  longest  straight  line  that  can  be  drawn  across  the 
circle?  Find  the  circumference  of  a 
circle  whose  radius  is  21  ft. 

4.  What  will  be  the  cost,  at  75/ 
per  yard,  of  carpeting  a  stairway  of 
18  steps,  the  tread  of  each  stair  being 
12  in.  and  the  riser  8  in.  ?  (Allow  for 
one  extra  step  and  one  extra  riser.) 

5.  How  many  telegraph  poles  10  rd.  apart  will  be  required 
for  150  mi.  of  railroad  ? 

Areas 

oral  exercise 

1.  What  is  the  area  of  a  square  1  rd.  on  each  side  ? 

2.  How  many  squares  1  rd.  on  each  side  in  a 
rectangle  6  rd.  long  and  1  rd.  wide  ? 

3.  How  many  rectangles, 
each  6  rd.  by  1  rd.,  in  a  rec- 
tangle 6  rd.  by  3  rd.  ? 

4.  How  many  square  rods 
in  the  area  of  a  rectangle  6  rd. 
long  and  3  rd.  wide  ? 

5.  How  many  square  rods 
in  the  area  of  a  rectangle  16  rd. 
long  and  132  ft.  wide  ?  6?d: 

Solution.    132  ft.  =  8  rd.   A  rectangle       132  f t.  =  8  rd. 
1  rd,  on  a  side  contains  1  sq.  rd.    But  the       8  X  16  SO    rd  =  128  SQ    rd 
given  rectangle  is  16  times  1  rd.  long  and 
8  times  1  rd.  wide.  Therefore  the  required  area  is  16  x  8  x  1  sq.  rd.,  or  128  sq.  rd. 

227.    The  product  of  the  length  and  ividth  of  a  rectangle  equals 

the  area. 

ORAL   EXERCISE 

Find  the  areas  of  rectangles  having  the  following  dimensions. 
Make  use  of  the  short  method  explained  in   §§  180-182. 
1.   ^  ft.  by  ^  ft.  3.    9.5  rd.  by  9.5  rd. 


t 

6rd. 

i. 

CO 

2. 


7|  rd.  by  71  rd. 


4.    12.5  ft.  by  4.5  ft. 


204 


PRACTICAL   BUSINESS   ARITHMETIC 


228.  The  dimensions  of  a 
triangle  are  the  base,  the  side 
on  which  the  triangle  appears 
to  stand ;  the  altitude,  the  per- 
pendicular distance  from  the 
base  to  the  highest  point  of 
the  triangle. 


Base 


ORAL   EXERCISE 


1.    How  does  the  area  of  the  triangle  on  the  right  compare 
with  the  area  of  a  rectangle  8  ft.  by  4  ft.  ? 

2.  Compare  the  area  of  the  triangle  on  the  left  with 
the  area  of  a  rectangle  12  rd.  by  5i  rd. 

3.  What  is  the  area  of  a  triangle 
whose  base   is   8  ft.  and  whose  alti- 

Dj^dT     tude  is  9i  ft.  ? 

229.    In  the  above  exercise  it  is  clear  that  one  half  the  product 
of  the  base  and  altitude  of  a  triangle  equals  the  area. 


ORAL    EXERCISE 

State  the  areas  of  triangles  whose  bases  and  altitudes,  respec- 
tively, are  as  follows  : 

1.  20  ft.,  18  ft.  3.    12  ft,  41  ft. 

2.  12  ft.,  16  ft.  4.    191  ft.,  8  ft. 

230.    If  a  circle  be  divided  as  in  the  figure  on  the  left  and  the 
parts  rearranged  as  in  the  figure  on  the  right,  it  will  be  clear 
that  the  area  of  the  circle   equals  the   area 
of    the    twelve    triangles.     The    altitude    of 


each  triangle  is  the  radius  of  the  circle,  and  the  sum  of  the 
bases  the  circumference. 

231.    It  is  therefore   clear  that  one  half  the  product  of  the 
circumference  and  radius  of  a  circle  equals  the  area. 


PRACTICAL   MEASUEEMENTS 


205 


ORAL  EXERCISE 

1.  Find  the  area  of  this  triangle:  base,  8  in.;  height,  11  in. 

2.  A  field  contains  1280  sq.  rd.     If  the  width  is  32  rd.,  what 
is  the  length  ? 

3.  A  man  sold  a  lot  10  rd.  long  and  8  rd.  wide  at  the  rate  of 
$260  per  acre.     How  much  did  he  receive  ? 

WRITTEN  EXERCISE 

1.  Find  the  area  of  a  circular  pavilion  with  a  radius  of  56i  ft. 

2.  A  city  lot  contains  ^  A.     If  it  is  200  ft.  long,  what  is  its 
width,  and  what  is  its  value  at  50  /  per  square  foot  ? 

3.  The  floor  of  a  restaurant  50  ft.  long  and  40  ft.  wide  is  cov- 
ered with  tiles  8  in.  square.     How  many  tiles  will  be  required  ? 

4.  A  park,  50  rd.  long  and  40  rd.  wide,  has  a  walk  1  yd.  wide 
inclosing  it.     How  many  square  feet  in  the  walk  ? 

Public  Lands 

232.  In  parts  of  the  United  States  public  lands  are  surveyed 
by  selecting  a  principal  meridian  which  runs  north  and  south,  and 
a  base  line  which  runs  east  and  west.  l.  ]^ 
Other  lines  divide  the  land  into  tracts 
6  mi.  square  called  townships.  Town- 
ship lines  running  north  and  south  are 
called  ranges. 

A  in  the  diagram,  may  be  read  as 
Tp.  1  N.,  R.  3  W. :  the  first  township  north 
of   the  base  line,  in  the  third  range  west   of   the   principal   meridian. 

233.  Each  townsliip  is  divided  into  36  sections,  each  1  mi. 
square.  The  numbering  of  a  section 
is  shown  in  the  diagram  at  the  left. 

Sections  are  divided  into  halves  and 
quarters;  quarter  sections  are  subdivided 
into  halves  and  quarters. 

If  diagram  3  is  B  of  diagram  2,  and 
diagram  2  is  A  of  diagram  1,  C  of  dia- 


W- 


g 

1 

■ 

1 

Base  a 

Line 

^ 

1 

3 

6 

5 

4 

3 

2 

1 

r 

8 

9 

10 

11 

12 

18 

17 

16 

15 

14 

13 

B 

20 

21 

22 

23 

24 

80 

29 

28 

27 

2C 

25 

31 

32 

33 

34 

35 

36 

3 

N.  i         Section 
(320  A.) 

S.W.  i 
(160  a.) 

li 

Township 


Section 


gram  3  may  be  described  as  the  S.  E.  1  of  S.  E.  i,  Sec.  19,  Tp.  1  N.,  R.  3  W. 


206  PRACTICAL  BUSINESS  ARITHMETIC 

ORAL  EXERCISE 

1.  How  many  chains *n  a  mile  ?  liow  many  rods  ?  how  many 
feet  ?     How  many  rods  in  a  chain  ?  how  many  feet? 

2.  How  many  acres  in  a  field  50  ch.  by  40  ch.?  in  a  field 
40  ch.  square  ?  in  a  field  80  ch.  by  80  ch.  ? 

3.  A  field  has  an  area  of  4  A.  If  it  is  10  ch.  long,  how  wide 
is  it  and  what  will  it  cost  to  fence  it  at  50  ^  per  rod  ?  at  60  ^  ? 

WRITTEN   EXERCISE 

1.  Make  a  diagram  of  a  township  and  locate  N.  J,  Sec.  20. 

2.  Draw  a  diagram  illustrating  principal  meridian,  base  line, 
range  line,  and  township  lines,  and  mark  Tp.  2  S.,  R.  2  E.  and 
Tp.  1  N.,  R.  3  W. 

3.  Find  the  value,  at  112.50  per  acre,  of  Tp.  2  N.,  R.  3  W. 

4.  Find  the  cost  at  S25  per  acre  of  the  E.  h  of  N.W.  i,  Sec. 
20,  Tp.  1  N.,  R.  4  W. 

Squaiie  Root  and  Its  Applications 
oral  exercise 

1.  What  is  meant  by  factor^  by  exponent P  by  power  of  a 
number  f 

2.  State  the  second  power  of  each  of  the  following  numbers  : 
1,  2,  3,  4,  5,  6,  7,  8,  9.     How  much  is  122,  132^  142^  152^  162? 

3.  Name  one  of  the  two  equal  factors  of  each  of  the  following 
numbers:  2,  4,  9,  16,  25,  36,  49,  64,  81,  100,  121,  144,  169,  196. 

234.  The  square  of  a  number  is  the  product  arising  from 
using  the  number  twice  as  a  factor.  The  square  root  of  a  number 
is  one  of  the  two  equal  factors  of  the  number. 

235.  The  square  root  of  a  number  may  be  indicated  by  writ- 
ing the  number  under  the  radical  sign  ■y/~  or  by  placing  the 
fraction  ^  above  and  to  the  right  of  the  number. 

Thus,  \/l96  or  1965  indicates  the  square  root  of  196. 

236.  The  square  root  of  a  number  is  readily  derived  from  the 
process  by  which  the  square  is  formed. 


PRACTICAL   MEASUREMENTS  207 

237.  Example.     What  is  the  square  of  42  ? 

Solution.     Since  42  =  40  +  2,  the  square  of  42  may  be  found  as  follows  : 

40  +  2 

40  +  2                 .  402=1600 

(40x2) +  22  2(40x2)=    160 

402  ■!_  (40x2)  22   = 4 

402+ 2(40x2)  + 22=  17(54- 

238.  In  the  preceding  process  it  is  shown  that  the  square  of 
a  number  is  equal  to  the  square  of  the  tens  plus  twice  the  product 
of  the  tens  hy  the  units,  plus  the  square  of  the  units. 

239.  12  =  1 ,  102  ^  100,  1002  =  10000,  and  so  on ;  92  =  81,  992  ^ 
9801,  9992=  998001,  and  so  on.  If  is  therefore  evident  that  the 
square  of  an  integral  number  contains  twice  as  many  figures  or 
one  less  than  twice  as  many  figures  as  the  number.  Hence,  if 
an  integral  number  be  separated  into  groups  of  two  figures 
each,  from  right  to  left,  there  will  be  as  many  figures  in  the 
square  root  as  there  are  groups  of  figures  in  the  number. 

240.  Examples.   1.   What  is  the  square  root  of  529  ? 

Solution.     Beginning  at  the  right,  separate  the  number  into  5   29(23 

periods  of  two  figures  each.     The  greatest  square  in  5  is  4  and  a 

the  square  root  of  4  is  2,  the  tens'  figure  of  the  root.     Find  the  — — -— 

remainder,  affix  the  second  period,  and  the  result  is  129.    This    ^"^J^ 
remainder  is  equal  to  twice  the  product  of  the  tens  by  the  units,  1    29 

plus  the  square  of  the  units  (§  242).  Twice  2  tens  is  4  tens  (40) 
and  4  tens  (40)  is  contained  in  129,  3  times ;  hence,  3  is  the  units'  figure  of  the 
root.  Twice  the  tens  multiplied  by  the  units  plus  the  square  of  the  units  is  the 
same  as  twice  the  tens  plus  the  units  multiplied  by  the  units.  Therefore,  annex 
3  units  to  the  4  tens  and  multiply  by  3 ;  the  result  is  129.  The  square  root  of 
529  is  thus  shown  to  be  23. 

2.   What  is  the  square  root  of  (a)  13.3225;   (5)  of  .0961  ? 

13  .32  25(3.65  .09  61(.31 

9  .09 


6.6)4  .32  .61). 00  61 

3  .96  .00  61 


7.25)     .36  25 
.36  25 


208  PRACTICAL  BUSINESS  ARITHMETIC 

241.  The  process  of  finding  the  square  root  of  a  number  may 
be  summarized  as  follows  : 

Beginning  at  the  units,  sejparate  the  number  into  groups  of  two 
figures  each. 

Find  the  greatest  square  in  the  left-hand  group  and  write  its 
root  for  the  first  figure  of  the  required  root. 

Subtract  the  square  of  the  root  figure  from  the  left-hand  period 
and  annex  the  second  period  for  a  dividend. 

Take  twice  the  root  figure  already  founds  considered  as  tens^ 
and  divide  the  dividend  by  it. 

Annex  the  quotient  to  both  the  root  ayid  the  trial  divisor  and 
multiply  by  the  units. 

Continue  in  like  manner  until  all  the  periods  have  been  used. 
The  result  will  be  the  square  root. 

If  a  number  contains  a  decimal,  begin  at  the  decimal  point  and  indicate 
groups  to  the  left  for  the  integral  part  of  the  root,  and  to  the  right  for  the 
decimal  part  of  the  root.  If  the  last  period  on  the  right  of  the  decimal 
point  has  but  one  figure,  annex  a  decimal  cipher,  as  each  decimal  period 
must  contain  two  figures. 

To  find  the  square  root  of  a  common  fraction,  extract  the  square  root  of 
the  numerator  and  denominator  separately.  If  the  terms  of  the  fraction 
are  not  perfect  squares,  reduce  the  fraction  to  a  decimal  and  then  extract 
the  square  root. 

WRITTEN  EXERCISE 
Find  the  square  root  of: 


1.  324. 

5. 

576. 

9- 

9025. 

13. 

II- 

2.  484. 

6. 

1024. 

10. 

3364. 

14. 

Ml- 

3.  676. 

7. 

7225. 

11. 

70.56. 

15. 

MM- 

4.  729. 

8. 

3969. 

12. 

150.0625. 

16. 

fitffi- 

242.  It  has  been  seen  that  the  area  of  a  square  is  the  product 
of  its  two  equal  sides.  It  therefore  follows  that  the  square  root 
of  the  area  of  a  square  equals  one  of  its  sides. 

243.  The  hypotenuse  is  the  side  opposite  the  right  angle  in  a 
right  triangle. 


PRACTICAI^  MEASUREMENTS 


209 


244.  In  the  accompanying  illustration  it  will  be  seen  that  the 
square  on  the  hypotenuse  is  equal  to 
the  sum   of  the  squares  on  the  other 
sides.     Hence, 

245.  To  find  the  hypotenuse  take  the 
square  root  of  the  sum  of  the  squares  of 
the  base  and  altitude;  and 

246.  To  find  the  base  or  the  altitude 
take  the  square  root  of  the  difference  he- 
tiveen  the  squares  of  the  hypotenuse  and 
the  other  side. 


WRITTEN  EXERCISE 

1.  A  square  field  contains  6.625  A.     What  is  the  length  of 
one  of  its  sides  ? 

2.  Find  the  side  of  a  square  containing  the  same  area  as  a 
field  160  rd.  long  by  90  rd.  wide. 

3.  What  is  the  hypotenuse  of  a  right-angled  triangle,  the  base 
of  which  is  30  ft.  and  the  altitude  40  ft.  ? 

4.  The  accompanying  diagram,  represents 
a  piece  of  land.  It  is  drawn  on  the  scale  of 
-^-Q  in.  to  the  rod.  The  land  is  divided  into 
two  fields  by  the  line  AB.  Find  the  cost, 
at  50  ^  per  rod,  of  fencing  the  two  fields. 

5.  What  will  be  the  cost,  at  $1.75  per  chain,  of  fencing  a 
square  field  containing  1.6  A.? 


Roofing 

247.  Roofing  is  usually  measured  by  the  square  of  100  sq.  ft. 

248.  The  size  of  slates  used  for  roofing  varies  from  6  in.  by 
12  in.  to  16  in.  by  24  in. 

Contractors  and  builders  generally  use  prepared  tables  for  estimating  the 
amount  of  slate  to  be  used.  The  number  of  slates  per  square  varies  with 
the  size  of  the  slate.  Thus,  slates  16  in.  by  24  in.  require  86  per  square; 
slates  6  in.  by  12  in.  require  533  per  square ;  etc. 


210 


PRACTICAL   BUSINESS   ARITHMETIC 


'  249.  All  shingles  average  4  in.  in  width  and  are  put  up  in 
bundles  of  250.  The  shingles  most  commonly  used  are  16  in. 
or  18  in.  long.  16-inch  shingles  are  generally  laid  4^  in.  and 
18-inch  shingles  5^  in.  to  the  weather. 

250.  A  shingle  4  in.  wide  laid  41  in.  to  the  weather  will  cover 
18  sq.  in.  A  square  contains  14,400  sq.  in.  14,400  sq.  in.  'T- 
IS sq.  in.  =  800.  It  is  therefore  clear  that  800  16-inch  shingles 
will  cover  a  square  of  roof. 

251.  A  shingle  4  in.  wide  laid  5 1-  in.  to  the  weather  will  cover 
22  sq.  in.  14,400  sq.  in.  -^  22  sq.  in.  =  655.  It  is  therefore 
clear  that  655  IS-inch  shingles  will  cover  a  square  of  roof. 

In  practice  655  per  square  is  called  700  per  square. 


in  7500  shingles? 


ORAL  EXERCISE 

1.  How  many  bundles  in  1000  shingles 
in  26,000  shingles  ? 

2.  What  will  be  the  cost,  at  14  per 
square,  of  tinning  a  roof  20  ft.  by  15  ft.  ? 

3.  A  certain  roof  requires  7610  shingles. 
How  many  bundles  of  shingles  must  be 
bought  to  cover  it? 

A  dealer  will  not  sell  a  fractional  part  of  a 
bundle  of  shingles. 

4.  How  many  slates  at  300  to  the  square 
will  be  required  for  a  flat  roof  30  ft.  by 
20  ft.  ? 

252.  The  rise  in  the  -rafters  for  each 
foot  in  the  base  of  the  gable  is  called  the 
pitch  of  the  roof. 

253.  When  the  rise  of  the  roof  is  6  in. 
per  foot,  the  roof  is  said  to  have  one-fourth 
pitch. 

254.  When  the  rise  of  the  rafters  is  12  in.  per  foot,  the  roof 
is  said  to  have  one-half  pitch. 


Gothic  Pitch 


PRACTICAL   MEASUREMENTS 


211 


255.  When  the  rise  of  the  rafters  is  15  in.  per  foot,  the  roof 
is  said  to  have  five-eighths,  or  Gothic  pitch. 

When  the  rise  of  the  rafters  is  6  in.  per  foot,  the  perpendicular  height  of 
the  gable  is  i  of  the  width  of  the  building ;  when  the  rise  is  12  in.  per  foot, 
the  height  of  the  gable  is  ^  the  width  of  the  building;  when  the  rise  is  15 
in.  per  foot,  the  height  of  the  gable  is  f  of  the  width,  or  1^  times  |  the  width 
of  the  building.     Hence  the  names  one-fourth  pitch,  one-half  pitch,  etc. 


Find  the  height  of  the  gable  : 

Width  of  Building      Pitch  of  Roof 

Width  of  Building 

Pitch  of  Roof 

1.    30  ft.                   1 

3.     24  ft. 

Gothic 

2.    50  ft.         12  in.  per  ft. 

4.     36  ft. 

i 

WRITTEN  EXERCISE 

1.  The  accompanying  diagram  represents  the  roof  of  a  shed 
16  ft.  wide.     If  the  ridge- 
pole is  68  ft.,  the  pitch  of 
the  roof  one  half,  and  the 
projection  of   the  rafters 
18  in.,  how  many  shingles 
16  in.  long,  laid  ^  in.  to  TfilillPlIi™ 
the  weather,  will  be  re-     |ll|jl 
quired  to  cover  the  roof  ? 

Solution 

\  of  16  ft.  =  8  ft.  =  the  base  of  the  triangle  ABC. 

The  pitch  of  the  roof  is  \  ;  ^  of  16  ft.  =  8  ft.  =  the  altitude  of  the  triangle  ABC. 

82  +  82  =  128  ;  128^  =  11.31,  number  of  feet  in  the  hypothenuse  of  ABC. 
18  in.  =  1.5  ft.  ;  11.31  ft.  +  1.5  ft.  =  12.81  ft.  =  the  length  of  the  rafters  or 
the  width  of  each  side  of  the  roof. 

2  X  68  X  12.81  ft.  =  1742.16  sq.  ft.  =  the  entire  surface  of  the  roof. 
1742.16  sq.  ft.  =  17.4216  squares ;  17.4216  x  800  shingles  =  13937  shingles. 
As  bundles  of  shingles  are  not  broken  it  will  be  necessary  to  buy  14000  shingles. 

2.  A  building  is  40  ft.  wide.  If  the  length  of  the  ridge- 
pole is  80  ft.  and  the  projection  of  the  rafters  20  in.,  how  many 
shingles  18  in.  long  and  laid  5^  in.  to  the  weather  will  be 
required  for  the  roof,  the  pitch  being  |  ? 


212  PRACTICAL   BUSINESS   ARITHMETIC 

3.  A  building  is  30  ft.  wide.  If  the  length  of  the  ridge- 
pole is  60  ft.  and  the  projection  of  the  rafters  15  in.,  how  many 
shingles  16  in.  long  and  laid  4^  in.  to  the  weather  will  be 
required  for  the  roof,  the  pitch  being  ^? 

Plastering 

256.  Plastering  is  usually  measured  by  the  square  yard. 

257.  There  is  no  uniform  rule  with  respect  to  the  allowance 
to  be  made  for  doors,  windows,  and  other  openings. 

What  Allowance,  if  any,  shall  be  made  for  openings  is  usually  stated  in 
the  contract  covering  the  work.  In  some  sections  it  is  customary  to  make 
allowance  for  one  half  the  area  of  the  openings ;  in  others,  for  the  full  area 
of  the  openings  ;  in  still  others,  for  a  stated  number  of  square  feet. 

In  giving  the  dimensions  of  a  room  carpenters,  architects,  and  mechanics 
write  the  length  first,  then  the  width,  and  finally  the  height.  They  also 
usually  write  5"  for  5  in.,  5'  for  5  ft.,  and  5'  x  5'  for  5  ft.  by  5  ft, 

ORAL   EXERCISE 

1.  What  is  the  perimeter  of  a  square  room  20'  on  a  side  ? 

2.  What  is  the  perimeter  of  a  dining  room  18'  x  12'  x  9'? 

3.  How  many  square  feet  in  the  four  walls  of  the  room  in 
problem  2,  not  allowing  for  openings  ?  in  the  ceiling  ?  in  the 
four  walls  and  the  ceiling  ? 

4.  How  many  square  yards  in  the  four  walls  of  a  room  24'  x 
16'  X  9',  not  allowing  for  openings? 

5.  At  25^  per  square  yard,  what  will  it  cost  to  plaster  945 
sq.  ft.  ?     1080  sq.  ft.  ?     1440  sq.  ft.  ? 

WRITTEN  EXERCISE 

1.  What  will  it  cost,  at  27  ^  per  square  yard,  to  plaster  the 
walls  and  ceiling  of  a  hall  60'  x  40^  x  24',  making  an  allow- 
ance of   40  sq.  yd.  for  openings  ? 

2.  Find  the  cost,  at  26^  per  square  yard,  of  plastering  the 
walls  and  ceiling  of  a  room  18'  x  16'  6"  x  8'  6'^  making  full 
allowance  for  2  doors  each  7'  6"  x  4',  3  windows  6'  x  4', 


PEACTICAL  MEASUREMENTS 


213 


3.  What  will  be  the  cost  of  plastering,  with  hard  finish,  at 
34  ^  per  square  yard,  the  walls  of  the  rooms  in  the  following 
dwelling  ? 

First  Floor.  Parlor,  14'  x  12'  ;  sitting  room,  12'  x  12' ; 
dining  room,  12'  x  10'  ;  kitchen,  12'  x  10' ;  pantry,  8'  x  6'. 
All  rooms  on  this  floor  are  uniformly  8'  6"  high. 

Second  floor.  Front  chamber,  14'  x  12'  ;  back  chamber, 
12'  X  12'  ;  middle  chamber,  10'  x  9'  ;  hall,  23'  x  4'.  All  rooms 
on  this  floor  are  uniformly  8'  high. 

Allowance  is  made  for  40  openings  of  17  sq.  ft.  each. 


Painting 

258.  Painting  is  usually  measured  by  the  square  yard. 

259.  It  is  customary  to  make  no  allowance  for  windows,  the 
painting  of  window  sills  and  sashes  being  considered  as  expen- 
sive as  the  painting  of  the  surface  area  of  the  entire  window. 

WRITTEN  EXERCISE 

1.  What  will  it  cost,  at  25^  per  square  yard,  to  paint  the 
walls  of  a  room  20'  x  16'  x  12',  no  allowance  being  made  for 
doors  or  windows  ? 

2.  At  6J^  per  square  yard,  what  will  it  cost  to  kalsomine  the 
walls  and  ceiling  of  a  room  24'  x  18'  x  12',  allowing  for  a  door 
9'  X  4',  2  windows  7'  x  4',  and  a  wainscot  3'  high  around  the 
regular  surface  of  the  room  ? 

3.  Find  cost,  at  24^  per  square  yard,  of  two  coats  of  paint 
on    the   outside  walls   of  a 

tobacco  barn  68'  x  20'  x  25' 
with  gables  extending  10' 
above  the  ends  of  the  walls. 

4.  What  will  be  the  cost, 
at  22^  per  square  yard,  of 
painting  the  outside  walls  of 
a  barn  100'  x  40'  x  20'  with  gables  extending  10'  above  the  walls  ? 
with  gables  extending  12|'  above  the  walls  ? 


214  PRACTICAL   BUSINESS  ARITHMETIC 

Flooring 

260.  Flooring  is  measured  by  the  square  (100  sq.  ft.)  or  by  the 
thousand  square  feet. 

Professional  floor  layers  charge  by  the  square,  the  price  being  from  75^  to 
$  1.50  per  square.     Carpenters  usually  work  by  the  day  in  laying  floors. 

Spruce  flooring  is  4"  or  5^"  in  width;  hardwood  flooring  is  2"  or  2^"  in 
width.  In  flooring  there  is  considerable  waste  in  forming  the  tongue  and 
the  groove  of  the  boards.  When  flooring  is  3"  or  more  in  width,  it  requires 
about  1^  sq.  ft.  of  material  for  every  square  foot  of  surface  to  be  covered; 
when  flooring  is  less  than  3"  in  width,  it  requires  1^  sq.  ft.  for  every  square 
foot  of  surface  to  be  covered. 

261.  Example.  How  many  feet  of  spruce  flooring  will  be 
required  for  a  room  32'  x  24'? 

Solution.     32  x  24  =  768,  the  number  of  square  feet  to  be  covered. 

1^  X  768  sq.  ft.  =  060  sq.  ft.,  the  quantity  of  flooring  required. 

WRITTEN    EXERCISE 

1.  Find  the  cost  at  845  per  thousand  square  feet  of  a  hard- 
wood floor  for  a  room  20'  x  16'. 

2.  A  pavilion  is  70'  x  50'.  If  the  flooring  is  of  spruce,  what 
will  be  the  cost  at  $  27  per  thousand  square  feet  ? 

3.  In  a  two-story  dwelling  the  floor  area  measures  S5'6"  x  26'. 
The  first  floor  is  to  be  of  hardwood  and  the  second  floor  of  spruce. 
Find  the  quantity  of  flooring  needed. 

4.  What  will  be  the  cost  of  a  hardwood  floor  in  a  room 
30' X  28',  if  the  labor  and  incidentals  cost  825.50,  the  lumber 
S48perM.? 

5.  Find  the  cost  of  laying  an  oak  floor  20'  x  15',  reckoning 
the  labor  and  incidentals  at  $  9.50,  the  floor  boards  at  $  83|^  per 
thousand. 

6.  The  floors  in  a  three-story  dwelling  are  each  55'  4"  x  33' 
10".  The  first  floor  is  to  be  of  hardwood  worth  1 50  per 
thousand  square  feet  and  the  other  floors  of  spruce  worth  $27 
per  thousand  square  feet.  If  it  costs  11.10  per  square  for 
labor,  what  will  be  the  total  cost  of  laying  the  three  floors  ? 


PRACTICAL   MEASUREMENTS 


215 


Carpeting 

262.  Carpet  is  sold  by  the  yard.  Such  floor  covering  as 
oilcloth  and  linoleum  are  frequently  sold  by  the  square  yard. 

263.  In  determining  the  number  of  yards  of  carpeting  re- 
quired for  a  room  it  is  necessary  to  know  whether  the  strips 
are  to  run  lengthwise  or  crosswise. 

Carpets  are  generally  laid  lengthwise  of  a  room  ;  but  when  the  matter  of 
expense  is  an  item,  it  is  sonxetimes  more  economical  to  lay  the  strips  cross- 
wise. 

When  the  length  of  the  strips  required  is  not  an  even  number  of  yards, 
there  is  usually  some  waste  in  matching  the  pattern.  Merchants  will  cut 
fractional  lengths  but  not  fractional  widths  of  carpeting.  It  is  therefore 
frequently  necessary  to  cut  off  or  turn  under  a  part  of  a  strip. 

ORAL   EXERCISE 

1.  How  many  yards  of  carpet,  1  yd.  wide,  must  be  purchased 
for  a  room  5  yd.  long  by  4  yd.  wide  ? 

2.  The  accompanying  diagram  represents  a 
room  drawn  on  the  scale  of  21  of  an  inch  to 
the  foot.     Find  the  dimensions  of  the  room. 

3.  How  many  strips  of  carpet,  1  yd.  wide, 
laid  lengthwise  of  the  room,  will  be  required 
for  problem  2  ?  How  many  feet  in  each  strip  ?    How  many  yards 
of  carpet  will  be  required  for  the  room  ? 

4.  The  accompanying  diagram  represents  a  room  drawn  on 
the  scale  of  ^  in.  to  the  foot. 
How  many  strips  of  carpet, 
1  yd.  wide,  laid  lengthwise 
of  the  room,  will  be  required 
to  cover  it  ?  What  part  of 
a  strip  must  be  cut  off  or 
turned  under  in  this  case? 

5.  How  many  feet  in  each 
strip  in  problem  4  ?  If  there  is 

1  .  1  2  in. 

no  waste  in  matching  the  pat- 
tern, how  many  feet  of  carpet  will  be  required  ?  how  many  yards  ? 


lin. 


216 


PRACTICAL   BUSINESS  ARITHMETIC 


WRITTEN   EXERCISE 

1.  How  many  yards  of  carpeting  1  yd.  wide  will  be  required 
to  cover  the  chamber  in  the  accompanying  floor  plan  if  the  strips 
are  to  run  lengthwise  and  there  is 
no  waste  in  matching  the  pattern  ? 

2.  Find  the  number  of  yards  of 
carpet  required  to  cover  the  room 
in  problem  1  if  the  strips  run  across 
the  room  and  there  is  a  waste  of 
6  in.  per  strip  in  matching  the 
pattern. 

3.  If  the  chamber  is  carpeted  in 
the  more  economical  way,  what  will 
be  the  cost  at  $  1.25  per  yard  ? 

4.  How  many  yards  of  carpet 
I  yd.   wide   will   be   required   for 

the  parlor  in  the  foregoing  floor  plan  ?     The  strips  are  to  run 
lengthwise,  and  there  is  no  waste  in  matching  the  pattern. 

The  cheaper  grades  of  carpet  are  usually  1  yd.  wide.  The  expensive 
grades,  such  as  Brussels,  Wilton,  etc.,  are  |  yd.  wide. 

5.  How  many  yards  of  carpet  |  yd.  wide  will  be  required  for 
the  dining  room  in  the  foregoing  floor  plan  ?  The  strips  are  to 
run  lengthwise,  and  there  is  a  waste  of  6  in.  per  strip  in  match- 
ing the  pattern. 

Papering 
264.    Wall  paper  is  usually  sold  in  double  rolls  18  in.  wide 
and  16  yd.  long. 

Single  rolls  18  in.  wide  and  8  yd.  long  are  sometimes  used,  but  it  is 
generally  found  more  economical  to  use  double  rolls.  These  dimensions 
vary  more  or  less. 

Allowances  for  openings,  such  as  doors  and  windows,  are  made  in  dif- 
ferent ways  by  different  paper  hangers.  Some  make  a  uniform  allowance 
for  each  opening,  while  others  make  allowance  for  the  exact  measurements 
of  the  openings. 

Any  whole  rolls  left  over  after  papering  may  usually  be  returned  to 
the  dealer. 


PRACTICAL   MEASUREMENTS  217 

ORAL  EXERCISE 

1.  What  will  the  border  for  a  room  15'  x  18'  cost  at  33^  f 
per  yard? 

2.  18  in.  =  f  ft.  30  ft  -^  f  ft.  =  30  ft.  x  |  ft.  =  20.  Divide 
21  ft.  by  18  in. 

3.  A  wall  is  15  ft.  long  and  9  ft.  high.  If  there  are  no 
openings,  how  many  strips  will  be  required  to  cover  it  ?  How 
many  full  strips  can  be  cut  from  each  double  roll  of  paper? 
What  part  of  a  strip  will  run  to  waste?  How  many  rolls  will 
be  required  for  the  wall  ? 

4.  Suppose  that  in  problem  2  there  is  a  door  3'  x  8'.  What 
is  the  length  of  the  regular  surface  of  the  wall  ?  Fractional 
strips  must  be  counted  as  full  strips.  Why  ?  How  many 
strips  of  paper  will  be  required  to  cover  the  regular  surface  of 
the  wall  ?  Will  dealers  sell  a  fractional  part  of  a  roll  of 
paper?  How  many  rolls,  then,  will  be  required  for  the  regular 
surface  of  the  walls? 

5.  There  is  a  small  surface  over  the  door  in  problem  5  that 
has  not  been  considered.  What  may  be  used  to  cover  this 
surface  ? 

265.  Obviously,  to  estimate  the  quantity  of  paper  required 
for  a  room: 

From  the  perimeter  of  the  room  subtract  the  width  of  the  open- 
ings. Find  J  of  this  remainder  and  the  result  will  be  the  number 
of  strips  required.  Divide  the  number  of  strips  required  by  the 
number  of  full  strips  that  can  be  cut  from  each  roll  of  paper  and 
the  result  is  the  required  number  of  rolls. 

By  this  method  the  ends  of  the  rolls  are  supposed  to  be  utilized  for  the 
surface  above  the  doors  and  above  and  below  the  windows  and  other  irregu- 
lar places. 

The  height  of  the  room,  in  papering,  will  be  understood  to  mean  the 
distance  from  the  baseboard  to  the  frieze. 

To  estimate  the  paper  required  for  a  ceiling,  take  -|  of  the  width  of  the 
room  for  the  number  of  strips  required.  Divide  the  number  of  strips  re- 
quired by  the  number  of  full  strips  that  can  be  cut  from  each  roll  and  the 
result  is  the  number  of  rolls  of  paper  required. 


218  PEACTICAL   BUSINESS  AEITHMETIC 

266.  Example.  How  many  double  rolls  of  paper  will  be 
required  for  the  walls  and  ceiling  of  a  room  21'  x  18'  x  8',  al- 
lowing for  2  doors  and  3  windows,  each  3|-  ft.  wide? 

Solution 

(21'  +  18')  X  2  =  78',  the  perimeter  of  the  room. 

5x3^'  =  17|',  the  total  width  of  the  openings. 

78'  —  17|'  =  601' ,  the  perimeter  of  the  reguLar  surface  of  the  walls. 

I  of  60|  =  40i,  the  number  of  strips  of  paper  necessary  for  the  regular  surface. 

48'  -f-  8'  =  6,  the  number  of-  strips  in  each  roll. 

40i  strips  -=-  6  strips  =  6 if,  or  practically  7  rolls  of  paper  required  for  the  walls. 

I  of  18  =  12,  the  number  of  strips  required  for  the  ceiling. 

48'  -4-  21'  =  2f ,  or  practically  2,  the  number  of  strips  in  each  roll. 

12  strips  H-  2  strips  =6,  the  number  of  rolls  required  for  the  ceiling. 

6  rolls  +  7  rolls  =  13  rolls  required  for  the  walls  and  ceiling. 

WRITTEN  EXERCISE 

1.  The  rooms  in  the  floor  plan,  page  216,  are  9' high.  What 
will  it  cost,  at  93^  sl  roll,  to  paper  the  walls  and  ceiling  of  the 
parlor,  making  allowance  for  2  double  doors,  each  6'  wide,  1 
single  door  S^'  wide,  and  2  windows,  each  3 J'  wide? 

2.  How  many  rolls  of  paper  will  be  required  for  the  walls 
and  ceiling  of  the  dining  room  in  the  floor  plan,  page  216,  al- 
lowing for  1  double  door  6'  wide,  1  single  door  3^-'  wide,  and  2 
windows  each  3| '  wide  ? 

3.  At  43^  per  roll  how  much  will  it  cost  to  paper  the  walls 
and  ceiling  of  the  chamber  in  the  floor  plan,  page  216,  allowing 
for  2  windows,  each  3 J'  wide,  1  double  door  6'  wide,  and  1 
single  door  3|^'  wide. 

SOLIDS 

Rectangular  Solids 

267.  A  solid  is  that  which  has  lengthy  width, 
and  thickness. 

268.  A  rectangular  solid  is  a  solid  bounded 
by  six  rectangular  surfaces. 

269.  A  cube  is  a  rectangular  solid  having  six  square  faces. 


PRACTICAL   MEASUREMENTS 


219 


ORAL  EXERCISE 

1.    If  A  in  the  accompanying  series  of  diagrams  is  1  cu.  ft., 


how  many  cubic  feet  in  B  ?   in  C  ?   in  D  ? 


2.  How  many  cubic  feet  in  a  block  of  granite  6  ft.  long,  1  ft. 
wide,  and  1  ft.  high  ?  in  a  block  6  ft.  long,  3  ft.  wide,  and 
1  ft.  high ?  in  a  block  6  ft.  long,  3  ft.  wide,  and  3  ft.  high? 

3.  Find  the  volume  of  a  rectangular  solid  6  ft.  by  4  ft.  by  2 
ft. ;  a  rectangle  10  ft.  by  9  ft.  by  9  ft. 

-  4.    A  cellar  is  40  ft.  square  and  6  ft.  deep.     How  many  cubic 
yards  of  earth  were  removed  in  excavating  it  ? 

SoLTTTiON.    A  cube  1  ft.  on     6  X  40  X  40  X  1  CU.  ft.  =  9600  cu.  ft. 
the  side  contains  ]  cu.  ft.    The      qqqq  ^^^  f^.^  -  27  =  355|  CU.  yd. 
given  cube  is  40  x  1  ft.  long,  ^  '' 

40  X 1  ft.  wide,  and  6  x  1  ft.  high.     Therefore,  it  Contains  6  x  40  x  40  x  1  cu.  ft., 
or  9600  cu.  ft. ;  and  9600  cu.  ft.  =  355f  cu.  yd, ,  the  required  result. 

270.  In  the  foregoing  exercises  it  is  clear  that  the  product  of 
the  three  dimensions  of  a  solid  equals  the  volume  or  solid  contents. 

WRITTEN  EXERCISE 

1.  A  box  car  is  50  ft.  6  in.  long,  8  ft.  4  in.  wide,  and  3  yd. 
high.     What  is  its  volume  ? 

2.  A  piece  of  timber  is  60  ft.  long  and  18  in.  square.  How 
many  cubic  feet  does  it  contain  ? 

3.  A  village  constructs  a  reservoir  for  a  water  supply.  The 
length  is  100  yd.,  the  width  70  yd.,  and  the  depth  15  ft. 
What  will  be  the  cost,  at  23^  per  cubic  yard,  of  excavating  the 
reservoir  ? 


220  PEACTICAL   BUSINESS  ARITHMETIC 

Wood 

27^1.    Wood  is  measured  by  the  cord. 

272.  A  cord  of  wood  or  stone  is  a  pile  8  ft.  long,  4  ft.  wide, 
and  4  ft.  high.     It  con- 
tains 128  cu.  ft. 

The  word  "cord,"  as  prac- 
tically used  in  wood  measure, 
generally  means  a  pile  8  ft.  long 
and  4  ft.  high,  the  price  depend- 
ing on  the  length  of  the  stick.  ■^-a/m'C^- 

273.  Example.  How  many  cords  of  wood  in  a  pile  32  ft.  long, 
8  ft.  wide,  and  4  ft.  high  ? 

Solution.        ^toQ^     ~  ^ '  ^^^*  ^^'  there  are  8  cd.  in  the  pile. 
WRITTEN  EXERCISE 

1.  How  many  cords  in  a  pile  of  wood  60  ft.  long,  4  ft.  wide, 
and  6  ft.  high? 

2.  A  pile  of  wood  contains  5  cd.  If  it  is  4  ft.  wide  and  4  ft. 
high,  how  long  is  it  ? 

3.  A  pile  of  tan  bark  contains  150  cd.  If  it  is  4  ft.  wide 
and  8  ft.  high,  how  long  is  it  ? 

4.  A  pile  of  wood  .contains  8  cd.  It  is  64  ft.  long  and  as 
high  as  it  is  wide.     What  is  the  height  of  the  pile  ? 

Lumber 

274.  A  foot  of  lumber,  sometimes  called  a  board  foot,  is  a 
board  1  ft.  long,  12  in.  wide,-  and  1  in.  thick,  or  its  equivalent. 
An  exception  to  this  is  made  in  the  measurement  of  boards  less 
than  1  in.  in  thickness.  A  square  foot  of  the  surface  of  such 
boards  is  regarded  as  a  foot  of  lumber  regardless  of  the  thick- 
ness. Boards  more  than  one  inch  in  thickness,  planks,  joists, 
beams,  scantling,  and  sawed  timber  are  generally  measured  by 
the  board  foot. 


PEACTICAL   MEASUEEMENTS  221 

Thus,  a  board  12  ft.  long,  12  in.  wide,  and  1  in.  thick  contains  12  sq.ft. 
of  surface,  or  12  hoard  feet ;  a  board  12  ft.  long,  12  in.  wide,  and  \,  |,  or  |  in. 
thick  contains  12  sq.ft.  of  surface,  or  12  hoard  feet;  but  a  board  12  ft.  long, 
12  in.  wide,  and  2|  in.  thick  contains  30  hoard  feet. 

Scantling  is  timber  3|^  in.  wide  and  from  2  in.  to  4  in.  thick;  joists  are 
narrow  and  deep  sticks  of  lumber ;  planks  are  thick  boards ;  lumber  heavier 
than  joists  or  scantling  is  usually  called  timber. 

Except  when  sawed  to  order  and  in  cherry,  black  walnut,  etc.,  where  the 
price  is  15  ^  a  board  foot  and  upward,  the  width  of  a  board  is  reckoned  only 
the  next  smaller  half  inch.  Thus,  a  board  10 J  in.  wide  is  reckoned  as  10  in., 
and  a  board  lOf  in.  wide  is  reckoned  as  10^  in. 

The  average  width  is  used  in  measuring  boards  that  taper  uniformly. 
Thus,  a  tapering  board  12  ft.  long,  8  in.  wide,  at  one  end  and  6  in.  wide 
at  the  other  and  1  in.  thick  averages  7  in.  wide  and  contains  7  ft.  of 
lumber. 

ORAL  EXERCISE 

1.  How  many  square  feet  in  the  surface  of  a  board  12  ft. 
long,  8  in.  wide,  and  1  in.  thick  ?     How  many  board  feet  ? 

2.  How  many  board  feet  in  a  board  12  ft.  long,  4  in.  wide, 
and  I  in.  thick  ? 

3.  How  many  feet,  board  measure,  in  a  board  12  ft.  long, 
12  in.  wide,  and  2  in.  thick  ? 

4.  How  many  feet  of  lumber  in  65  boards  each  12  ft.  long, 
6  in.  wide,  and  1  in.  thick  ? 

275.  In  charging  or  billing  lumber  the  number  of  pieces  is 
entered  first ;  then  the  thickness  and  width  in  inches  and  the 
length  in  feet;  and  finally,  the  article. 

Thus,  in  billing  12  pc.  hemlock,  2  in.  thick,  6  in.  wide,  12  ft.  long,  the 
form  would  be :  12  pc.  2"  x  6",  12',  hemlock. 

ORAL  EXERCISE 

1.  How  many  board  feet  in  6  planks,  1|"  x  12",  W  2 

Suggestion.     By  inspection  eliminate  12  in  the  dividend. 
Then,  1^  x  6  x  14  =  126,  the  required  number  of  board  feet. 

2.  How  many  feet,  board  measure,  in  6  planks  2''  x  8'',  18'  ? 

Suggestion.     By  inspection  cancel  a  12  in  the  dividend  (6  x  2). 
Then,  8  x  18  =  144,  the  required  number  of  feet,  board  measure. 


222  PRACTICAL   BUSINESS  ARITHMETIC 

3.  How  many  feet  of  lumber  in  6  pc.  of  scantling  4'^  x  4'^  16'  ? 
Suggestion.     Mentally  picture  the  problem  arranged,  in  form  for  cancellation 

/6  X  4  X  4  X  16\  ^    Cancel  a  12  in  the  dividend  (^V  of  Fx4).    Then,  2  x  4  x  16, 

or  128,  equals  the  required  number  of  feet  of  lumber. 

4.  How  many  feet  of  lumber  in  5  sticks,  2''  x  6",  16'? 
Suggestion.       Mentally    picture    the    problem    in    form    for    cancellation 

/5  X  2  X  6  X  16\  ^    Q^^QQi  a  12  in  the  dividend  (J-  of  2ir6).     Then,  5  x  16,  or 

80,  equals  the  required  number  of  feet  of  lumber. 

5.  How  many  feet  of  lumber  in  a  plank  3''  x  12'',  16'?  in  6 
planks  ?  in  10  planks  ?  How  many  feet  of  lumber  in  a  plank 
2"  X  6",  12'  ?  in  5  planks  ?  in  20  planks  ? 

276.  Obviously,  the  number  of  board  feet  in  lumber  1  in.  or 
less  in  thickness  is  -^^  ^f  ^^^  product  of  the  length  in  feet  hy  the 
width  in  inches ;  and  the  number  of  board  feet  in  lumber  more 
than  1  in.  in  thickness  is  -^^  of  the  product  of  the  length  in  feet 
hy  the  width  and  thickness  in  inches.  But  the  work  may  be 
materially  shortened  by  mentally  cancelling  12  from  the  divi- 
dend as  illustrated  in  the  foregoing  exercise, 

ORAL  EXERCISE 

State  the  number  offeet^  hoard  measure^  in  the  following  hemlock: 

1.  5  pc,  3"  X  4",  14'.  13.      12  PC  2"  x    8",  18'. 

2.  6  pc,  2"  X  4",  20'.  14.        6  pc,  8"  x  10",  20'. 

3.  6  pc,  2"  X  6",  20'.  15.      30  pc,  2"  x    6",  20'. 

4.  20  pc,  2"  X  6",  14'.  16.  6  pc,  8"  x  10",  21'. 

5.  12  PC  2"  X  8",  14'.  17.  25  pc,  3"  x    8",  14'. 

6.  25  PC  3"  X  4",  12'.  18.  10  PC  2"  x    6",  13'. 

7.  25  pc,  2"  X  6",  20'.  19.  15  pc,  2"  x    6",  18'. 

8.  25  PC  3"  X  8",  16'.  20.  15  PC  2"  x    6",  12'. 

9.  10  PC  3"  X  4",  14'.  21.  16  pc,  2"  X    6",  10'. 

10.  10  pc,  2"  X  8",  18'.  22.     10  PC  8"  X  10",  15'. 

11.  14  PC  2"  X  6",  20'.  23.      15  PC  8"  x  10",  12'. 
'12.    10  pc,  3"  X  6",  20'.  24.    200  PC  2"  X    6",  20'. 


PRACTICAL   MEASUREMENTS  223 

WRITTEN  EXERCISE 

How  many  feet ^  hoard  7neasure,  in  each  of  the  following  f 

1.  100  joists,  4:"  X  4'^  16'.  4.    70  joists,  2"  x  10",  32'. 

2.  ^^  boards,  {"  x  6'',  12'.  5.      8  beams,  10"  x  10",  24'. 

3.  12  timbers,  8"  x  8",  40'.        6.    10  beams,  12"  x  12",  30'. 

7.  At  $  19  per  M,  find  the  total  cost  of  : 

6  joists,  2"  X  8",  12'.  5  joists,  2"  x  8",  18'. 

12  joists,  2"  X  8",  13'.  17  joists,  2"  x  6",  16'. 

30  joists,  2"  X  8",  15'.  30  joists,  2"  x  8",  16'. 

8.  At  $  26  per  M,  find  the  total  cost  of : 

7  beams,  9"  x  9",  20'.  16  beams,  9"  x  9",  18'. 

24  joists,  2"  X  10",  18'.  75  planks,  21"  x  8",  12'. 

150  boards,  |"  x  5",  12'.  576  boards,  1"  x  9",  16'. 

Cylinders 

277.  A  cylinder  is  a  solid  bounded  by  a  uniformly  curved 
surface  and  two  equal  parallel  circles.  ^,,g|j|||[||^^ 

Two  circles  are  parallel  when  all  the  points  of  |||II  |B 

one  are  equally  distant  fi-om  all  the  points  of  the  liii^^^  H       i  IIBI      i   ■  ' 

other.     The  curved  surface  of  a  cylinder  is  called  i"         '  ''^'    ||ii|HH|^^ 

its  lateral  surface  ;  the  parallel  circles  its  bases.  ^  v  ^tHI^^BRP™^ 

278.  If  the  lateral  surface  of  a  cylinder  be  exactly  covered 
with  paper,  it  will  be  found  that  the  paper  is  in  the  form  of  a 
rectangle  whose  length  and  width  are  equal  to  the  circumfer- 
ence and  height,  respectively,  of  the  cylinder.     Hence, 

The  product  of  the  circumference  and  height  of  a  cylinder  equals 
the  area  of  its  lateral  surface. 


ORAL  EXERCISE 

1.  If  the  accompanying  diagram  is  a  solid  4  ft.  square  and 
12  ft.  high,  what  is  the  area  of  its  six  sides? 

2.  Give  a  brief  rule  for  finding  the  entire  surface 
(lateral  surface  and  bases)  of  a  rectangular  solid  ;  of 
a  cylinder. 

3.  How  many  cubic  inches  in  a  block  2  in.  square 
and  1  in.  high?  in  a  block  2  in.  square  and  10  in.  high? 


lare  ana 


224  PRACTICAL   BUSINESS  ARITHMETIC 

279.  In  the  foregoing  exercise  it  is  clear  that  the  area  of  the 
base  multiplied  hy  the  height  of  the  cylinder  equals  the  volume. 

WRITTEN  EXERCISE 

■  1.    What  will  be  the  cost,  at  40^  per  cubic  yard,  of  excavat- 
ing for  a  cistern  10  ft.  in  diameter  and  23  ft.  deep  ? 

2.  A  man  dug  a  well  6  ft.  in  diameter  and  38  ft.  deep.  How 
much  should  he  receive  if  he  was  paid  |1  for  each  cubic  yard 
of  earth  removed  ? 

3.  What  will  be  the  cost,  at  12 J  ^  per  square  foot,  of  a  sheet- 
iron  smokestack  2^  ft.  in  diameter  and  30  ft.  high  ? 

Cisterns 

280.  A  gallon  equals  231  cu.  in. 

ORAL  EXERCISE 

1.  How  many  gallons  in  462  cu.  in.  ?     in  1386  cu.  in.  ? 

2.  How  many  gallons  of  water  in  a  vat  22  in.  long,  7  in. 
high,  and  3  in.  wide  ? 

3.  Give  a  rule  for  finding  the  exact  number  of  gallons  in  a 

vessel.     How  many  gallons  in  a  cubic  foot  ? 

Solution.  231  cu.  in.  =  1  gal.  1728  cu.  in.  =  1  cu.  ft.  Therefore,  1  cu.  ft. 
=  yg^jS-  gal.  =  7.48  +  gal.,  or  approximately  7|  gal. 

4.  Find  the  approximate  capacity,  in  gallons,  of  a  vat  5  ft. 
square  and  4  ft.  high. 

Solution.     5  f t.  x  5  ft.  x  4  f t.  =  100  cu.  ft.     100  times  71  gal.  =  750  gal. 

5.  State  a  rule  for  finding  the  approximate  capacity,  in  gal- 
lons, of  a  vessel. 

WRITTEN  EXERCISE 

Find  the  capacity  (^approximate  and  exact^,  in  gallons,  of: 

1.  A  cistern  6  ft.  square  and  12  ft.  deep. 

2.  A  cistern  6  ft.  in  diameter  and  10  ft.  deep. 

3.  A  tank  5  ft.  long,  4  ft.  wide,  and  6  ft.  deep. 

4.  A  cistern  15  ft.  in  diameter  and  20  ft.  deep. 


PRACTICAL   MEASUREMENTS  225 

Stone  Work 

281.  Stone  work  is  usually  measured  by  the  perch,  which  is 
a  mass  of  stone  16|  ft.  long,  1-|-  ft.  wide,  and  1  ft.  high,  contain- 
ing 24|  cu.  ft. 

In  some  localities  the  perch  contains  16^  cu.  ft. 

282.  Masonry  is  measured  by  the  cubic  yard  or  the  perch. 

In  measuring  stone  work,  such  as  the  walls  of  cellars  and  buildings, 
masons  take  the  distance  around  the  outside  of  the  wall  (the  girt)  for  the 
length.  In  this  way  the  corners  are  measured  twice,  but  this  is  considered 
offset  by  the  extra  work  required  in  building  the  corners. 

The  work  around  openings,  such  as  doors  and  windows,  is  also  more 
difficult  than  the  straight  work  and  on  this  account  no  allowance  is  usually 
made  for  openings,  unless  they  are  very  large. 

WRITTEN  EXERCISE 

1.  How  many  perches  of  stone  will  be  required  for  an  18-in. 
foundation  72' X  40'  x  10'? 

2.  How  many  perches  of  masonry  in  the  18-in.  walls  of  a 
cellar  40' X  30'  x  8' ? 

3.  How  many  cubic  yards  of  masonry  in  the  foundation  walls 
of  a  house  42'  x  32'  if  the  walls  are  21  ft.  wide  and  8  ft.  high? 
(Solve  (a)  by  mason's  and  (^)  by  actual  measure.) 

Brick  Work 

283.  A  common  brick  is  8  in.  long,  4  in.  wide,  and  2  in.  thick. 

Bricks  vary  in  size,  but  the  common  brick  may  be  taken  as  a  unit  for 
measuring  brick  work.  Contractors  and  builders  do  not  follow  any  uniform 
rule  for  estimating  the  number  of  bricks  required  for  a  wall.  It  is  suffi- 
ciently accurate,  however,  to  reckon  22  common  bricks,  laid  in  mortar,  for 
each  cubic  foot  of  wall.  In  estimating  material  for  a  brick  wall  actual 
measurements  are  taken  and  an  allowance  made  for  doors  and  windows  and 
other  openings.  In  estimating  labor  girt  measurements  are  taken  and 
usually  a  stated  allowance  made  for  openings  such  as  doors  and  windows. 
The  allowance  to  be  made  for  openings  is  generally  covered  by  contract 
In  some  localities  a  uniform  number  of  cubic  feet  is  deducted  for  each  open- 
ing ;  in  others  one  half  the  volume  of  all  openings  is  deducted ;  in  still  others 
nothing  whatever  is  deducted.  , 


226  PRACTICAL   BUSINESS  ARITHMETIC 

WRITTEN  EXERCISE 

1.  How  many  common  bricks  will  be  required  for  a  wall  84 
ft.  long,  161  ft.  high,  and  1|-  ft.  thick  ? 

2.  Find  the  cost  of  the  bricks  required  to  build  a  wall  300  ft. 
long,  12  ft.  high,  and  18  in.  thick,  at  $6  per  thousand. 

3.  How  many  bricks  will  be  required  for  the  four  walls  of  a 
building  80'  x  50'  x  25'  if  the  walls  are  18  in.  thick  and  500 
cu.  ft.  is  allowed  for  openings  ?  (Solve  (6?)  by  mason's  measure, 
making  allowance  for  the  openings,  and  (6  )  by  actual  measure.) 

CAPACITY 
Bins 

284.  The  stricken  bushel  is  used  in  measuring  grain.  The 
heaped  bushel  is  used  in  measuring  such  things  as  large  fruits, 
vegetables,  coal,  and  corn  on  the  cob.  A  stricken  bushel  equals 
2150.42  cu.  in.     A  heaped  bushel  equals  2747.71  cu.  in. 

ORAL  EXERCISE 

1.  How  many  bushels  of  wheat  in  2,150,420  cu.  in.  ? 

2.  State  a  rule   for   finding   the  exact  number   of  stricken 

bushels  in  a  bin.     What  part  of  a  stricken  bushel  is  1  cu.  ft.? 

8-4- 
SoLUTioN.     2150.42  cu.  in.  =  1  bu.,  stricken  measure.  ! _ 

1728  cu.  in.  =  1  cu.  ft.     Therefore,  1  cu.  ft.  =  172800-      2150.42)1728.000 

215042,  or  approximately  .8  of  a  bushel,  stricken  nieas-  ITzO  oob 

ure.  7664 

3.  Find  the  approximate  capacity,  in  stricken  bushels,  of  a 
cubical  bin  the  inside  of  which  measures  10  ft.  on  a  side ;  in 
cubic  inches  of  800  bu.  of  wheat. 

4.  State  a  brief  rule  for  finding  the  approximate  number  of 
stricken  bushels  in  a  bin;  the  approximate  number  of  cubic 
feet  in  any  number  of  stricken  bushels. 

5.  How  many  bushels  of  potatoes  in  a  bin  containing  2,747,710 
cu.  in.  ?  State  a  rule  for  finding  the  exact  number  of  heaped 
bushels  in  any  number  of  cubic  inches.  Reduce  a  cubic  foot 
to  a  decimal  of  a  heaped  bushel. 


PEACTICAL   MEASUEEMENTS  227 

.63- 
SoLUTiON.     2747. 71  cu.  in.  =  lbu.,  heaped  measure.    2747.71)1728.0000 
Therefore  1  cu.  ft.  =  172800  -h  274771,  or  approxi-  1648  626 

mately  .63  of  a  bushel,  heaped  measure.  ■ —       oTAri 

82  4313 

6.  Find  the  approximate  capacity,  in  heaped  bushels,  of 
1000  cu.  ft. ;    in  cubic  feet,  of  630  bu. 

7.  State  a  short  method  of  reducing  cubic  feet  to  heaped 
bushels;   heaped  bushels  to  cubic  feet. 

8.  Find  («)  the  exact  capacity  and  (6)  the  approximate 
capacity,  in  stricken  bushels,  of  a  bin  10^  X  5'  x  4^ 

Solutions 
(a)  10'  X  5'  X  4'  =  200  cu.  ft.  (6)  10'  x  5'  x  4'  =  200  cu.  ft. 

200  X  1728  cu.  in.  =  345,600  cu.  in.  .8  of  200  cu.  ft.  =  160  bu. 

345,600  cu.  in.  --  2150.42  =  165.31  +  bu. 

ORAL    EXERCISE 

1.  Find  the  approximate  capacity  in  bushels  of  a  wheat  bin 
10  ft.  long,  8  ft.  wide,  and  5  ft.  high. 

2.  A  square  bin  10  ft.  high  contains,  by  approximate  measure- 
ments, 800  bu.    What  is  its  width  ? 

3.  Approximately,  how  many  bushels  of  potatoes  may  be 
stored  in  a  bin  10  ft.  long,  5  ft.  wide,  and  4  ft.  high  ? 

WRITTEN   EXERCISE 

Find  the  approximate  capacity  in  stricken  bushels, of : 

1.  A  bin  12  ft.  square  and  4  ft.  deep. 

Inside  dimensions  are  given  in  all  the  problems  of  this  and  similar 
exercises. 

2.  A  box  6  ft.  long,  2i  ft.  wide,  and  3i  ft.  deep. 

3.  A  farmer  wishes  to  construct  a  square  granary  15  ft.  on 
each  side  that  will  hold  800  bu.  of  grain.  How  deep  must  the 
bin  be  made  ?     (Approximate  rule.) 

4-5.  Find  the  exact  capacity,  in  stricken  bushels,  of  prob- 
lems 1-2. 

6-7.  Find  the  approximate  capacity,  in  heaped  bushels,  of 
problems  1-2. 


228  PRACTICAL   BUSINESS  ARITHMETIC 

CALCULATION   TABLES 

285.  Persons  who  have  a  great  deal  of  computing  to  do 
frequently  use  machines  (see  Appendix  A)  and  calculation 
tables  to  aid  them  in  their  work.  The  table  on  page  229  will 
give  a  good  idea  of  the  arrangement  of  calculation  tables  that 
are  used  in  making  up  and  proving  bills  and  invoices,  comput- 
ing wages,  finding  percentages,  etc.  The  following  examples 
will  illustrate  a  few  of  the  many  uses  of  such  tables. 

286.  Examples,     i.    Multiply  58  by  42. 

Solution.     Under  58  and  opposite  42  find  2436. 

2.  How  many  square  feet  in  a  floor  88'  x  46'  ? 
Solution.     Under  46  and  opposite  38  find  1748  ;  that  is,  1748  sq.  ft. 

3.  Find  the  cost  of  495  yd.  wash  silk  at  39^. 
Solution.     Under  495  and  opposite  39  find  19,305  ;  that  is,  $  193.05. 

4.  Find  the  cost  of  48,000  bricks  at  14.95  per  M. 

Solution.  Under  495  and  opposite  48  find  23,760.  Since  the  zeros  in 
48,000  have  been  rejected,  there  are  but  two  places  to  point  off.     Result  $  237.60. 

5.  Find  the  cost  of  46  hr.  of  labor  at  25|  ^  per  hour. 

Solution.  Under  46  and  opposite  25  find  1150  ($11.50);  under  46  and 
opposite  I  find  34.50  (35  ;*).     $  11.50  +  35  ^  =  $  11.85,  the  required  result. 

ORAL  EXERCISE 

By  the  aid  of  the  table  state  the  product  of: 

1.  27  X  26.       5.    39  X  27.         9.    87  x  46/. 

2.  27x58.       6.    45x58.       lo.    93x32/. 

3.  45x46.       7.    37x46.       ii     48x93/. 

4.  47x39.       8.    49x58.       12.   47x87/. 

17.  Find  the  cost  of  49,500  lb.  of  old  rags  at  |/. 

18.  Find  the  cost  of  93,000  bricks  at  'f  5.25  per  M. 

19.  Find  the  cost  of  37  days'  labor  at  $1.35  per  day ;  at  15.25. 

20.  Find  the  cost  of  109  hours'  labor  at  27/;  at  39jZ^;  at  46  /. 

21.  Find  the  cost  of  49,500  lb.  freight  at  31  /  per  hundred- 
weight ;  of  46,000  lb.  at  27  /  per  hundredweight. 


13. 

35  x  93/. 

14. 

93  X  42/. 

15. 

46x87^. 

16. 

38  X  93/. 

PRACTICAL   MEASUREMENTS 


229 


CALCULATION  TABLE 


lulti- 
plier 

27 

39 

46 

68 

Multi- 
plier 

87 

93 

109 

128 

Multi- 
plier 

135 

147 

495 

625 

Multi- 
plier 

1 

27 

39 

46 

58 

1 

87 

93 

109 

128 

1 

135 

147 

495 

4 

1 

2 

54 

78 

92 

116 

2 

174 

186 

218 

256 

2 

270 

294 

990 

1050 

2 

3 

81 

117 

138 

174 

3 

261 

279 

327 

384 

3 

405 

441 

1485 

1575 

3 

4 

108 

156 

184 

232 

4 

348 

372 

436 

512 

4 

&40 

588 

1980 

2100 

4 

6 

135 

195 

230 

290 

5 

435 

465 

545 

640 

5 

675 

735 

2475 

2625 

5 

6 

162 

234 

276 

348 

6 

522 

558 

654 

768 

6 

810 

882 

2970 

3150 

6 

7 

189 

273 

322 

406 

7 

609 

651 

703 

896 

7 

045 

1029 

3465 

3675 

7 

8 

216 

312 

368 

464 

8 

696 

744 

872 

1024 

8 

1080 

1176 

3%0 

4200 

8 

9 

243 

351 

414 

522 

9 

783 

837 

981 

1152 

9 

1215 

1323 

4455 

4725 

9 

10 

270 

390 

460 

580 

10 

870 

930 

1090 

1280 

10 

1350 

1470 

4950 

5250 

10 

11 

297 

429 

506 

638 

11 

957 

1023 

1199 

1408 

11 

1485 

1617 

5445 

5775 

11 

13 

324 

468 

552 

696 

12 

1044 

1116 

13(»8 

1536 

12 

1620 

1764 

5940 

6300 

12 

13 

351 

507 

598 

754 

13 

1131 

1209 

1417 

1664 

13 

1755 

1911 

6435 

6825 

13 

14 

378 

546 

644 

812 

14 

1218 

1302 

1526 

1792 

14 

1890 

2058 

6930 

7350 

14 

16 

405 

585 

690 

870 

15 

1305 

1395 

1635 

1920 

15 

2025 

2205 

7425 

7875 

15 

16 

432 

624 

736 

928 

16 

1392 

1488 

1744 

2048 

16 

2160 

2a52 

7920 

84(10 

16 

17 

459 

663 

782 

986 

17 

1479 

1581 

1853 

2176 

17 

2295 

2499 

8415 

8925 

17 

18 

486 

702 

828 

1044 

18 

1506 

1674 

1962 

2304 

18 

2430 

2646 

8910 

9450 

18 

19 

513 

741 

874 

1102 

19 

1653 

1767 

2071 

2432 

19 

2565 

2793 

9405 

9975 

19 

20 

540 

780 

920 

IIGO 

20 

1740 

1860 

2180 

2560 

20 

2700 

2940 

9900 

10500 

20 

21 

567 

819 

966 

1218 

21 

1827 

1953 

2289 

2688 

21 

2835 

3087 

10395 

11025 

21 

22 

594 

858 

1012 

1276 

22 

1914 

2046 

2398 

2816 

22 

2970 

3234 

10890 

11550 

22 

23 

621 

897 

1058 

1334 

23 

2001 

2139 

2507 

2944 

23 

3105 

3381 

11385 

12075 

23 

24 

648 

936 

1104 

1392 

24 

2088 

2232 

2616 

3072 

24 

3240 

3528 

11880 

12600 

24 

25 

675 

975 

1150 

1450 

25 

2175 

2325 

2725 

3200 

25 

3375 

3675 

12375 

13125 

25 

26 

702 

1014 

1196 

1508 

26 

2262 

2418 

28^4 

3328 

26 

3510 

3822 

12870 

13650 

26 

27 

729 

1053 

1242 

15^56 

27 

2349 

2511 

2943 

3456 

27 

3645 

3969 

13365 

14175 

27 

28 

756 

1092 

1288 

1624 

28 

2436 

2604 

3052 

3584 

28 

3780 

4116 

13860 

14700 

28 

29 

783 

1131 

ia34 

1682 

29 

2523 

2697 

3161 

3712 

29 

3915 

4263 

14355 

15225 

29 

30 

810 

1170 

1380 

1740 

30 

2610 

2790 

3270 

3840 

30 

4050 

4410 

14850 

15750 

30 

31 

837 

1209 

1426 

1798 

31 

2697 

2883 

3379 

3968 

31 

4185 

4557 

15345 

16275 

31 

32 

864 

1248 

1472 

1856 

32 

2784 

2976 

3488 

4096 

32 

4320 

4704 

15840 

16800 

32 

33 

891 

1287 

1518 

1914 

33 

2871 

3069 

3597 

4224 

33 

4455 

4851 

16335 

17325 
17850 
18375 

33 

34 

918 

1326 

1564 

1972 

34 

2958 

3162 

3706 

4352 

34 

4590 

4998 

16830 

34 

35 

945 

1365 

1610 

2030 

35 

3045 

3255 

3815 

4480 

35 

4725 

5145 

17325 

35 

36 

972 

1404 

1G56 

2088 

36 

3132 

3348 

3924 

4608 

36 

4860 

5292 

17820 

18900 
19425 
19950 

36 

37 

999 

1443 

1702 

2146 

37 

3219 

3441 

4033 

4736 

37 

4995 

5439 

18315 

37 

38 

1026 

1482 

1748 

2204 

38 

a306 

3534 

4142 

4864 

38 

5130 

5586 

18810 

38 

39 

1053 

1521 

1794 

2262 

39 

3393 

3627 

4251 

4992 
5120 

39 

5265 

5733 

19305 

20475 

39 

40 

1080 

1560 

1840 

2320 

40 

3480 

3720 

4360 

40 

5400 

5880 

19800 

21000 

40 

41 

1107 

1599 

1886 

2378 

41 

3567 

3813 

4409 

5248 

41 

5535 

6027 

20295 

21525 

41 

42 

1134 

1638 

1932 

2436 

42 

36&4 

3906 

4578 

5376 

42 

5670 

6174 

20790 

22050 

42 

43 

1161 

1677 

1978 

2494 

43 

3741 

3999 

4687 

5504 

43 

5805 

6321 

21285 

22575 

43 

44 

1188 

1716 

2024 

2552 

44 

3828 

4092 

4796 

5632 

44 

5940 

6468 

21780 

23100 

44 

45 

1215 

1755 

2070 

2610 

45 

3915 

4185 

4905 

5760 

45 

6075 

6615 

22275 

23625 

45 

46 

1242 

1794 

2116 

2668 

46 

4002 

4278 

5014 

5888 

46 

6210 

6762 

22770 

24150 

46 

47 

1269 

1833 

2162 

2726 

47 

4089 

4371 

5123 

6016 

47 

6345 

6909 

23265 

24675 

47 

48 

1296 

1872 

2208 

2784 

48 

4176 

4464 

5232 

6144 

48 

6480 

7056 

23760 

25200 

48 

49 

1323 

1911 

2254 

2842 

49 

4263 

4557 

5341 

6272 

49 

6615 

7203 

24255 

25725 

49 

50 

1350 

1950 

2300 

2900 

60 

Multi- 
plier 

4350 

4650 

5450 

6400 

60 

6750 

7350 

24750 

26250 

60 

Multi- 
plier 

27 

39 

46 

68 

87 

93 

109 

128 

Multi- 
plier 

135 

147 

495 

525 

Multi- 
plier 

Vs 

3  38 

488 

5  75 

7  25 

Vs 

10  88 

1163 

13  63 

16  00 

Vs 

16  88 

18  38 

6188 

65  63 

Vs 

V4 

6  75 

9  75 

1150 

14  50 

¥4 

2175 

23  25 

27  25 

32  00 

V4. 

33  75 

36  75 

123  75 

13125 

V4 

% 

10  13 

14  63 

17  25 

2175 

% 

32  63 

34  88 

40  88 

48  00 

% 

50  63 

5513 

185  63 

196  88 

//« 

V2 

13  50 

19  50 

23  00 

29  00 

H 

43  5C 

46  50 

54  50 

64  00 

V2 

67  50 

73  50 

247  50 

262  50 

V2 

% 

16  88 

24  38 

28  75 

36  25 

% 

54  38 

58  13 

6813 

80  00 

% 

84  38 

9188 

309  38 

328  13 

% 

% 

20  25 

29  25 

34  50 

43  50 
50  75 

% 

65  2S 

69  75 

8175 

96  00 

% 

10125 

110  25 

37125 

393  75 

»/4 

Vs 

23  63 

3413 

40  25 

% 

76  13 1  81  38 

95  38 

112  00 

% 

,118  13 

128  63 

43313 

459  38 

Vs 

230  PEACTICAL  BUSINESS   ARITHMETIC 

22.  Find  the  cost  of  48,000  ft.  of  lumber  at  f  16  per  M  ;  of 
93,000  ft.  ;  of  52,500  ft. ;  of  49,500  ft. ;  of  58,000  ft. 

23.  An  agent  sold  240  (10  x  24)  excursion  tickets  at  $4.95. 
How  much  did  he  receive  ?     360  x  15.25  =  ?     310  x  il.47  =  ? 

24.  Find  the  cost  of  45  rm.  of  paper  at  11.35  ;  at  1 1.28  ;  at 
$1.09;  at  93^;  at  $4.95.  Also  find  the  cost  of  38  rm.  at  each 
of  the  above  prices ;  of  29  rm.  ;  of  37  rm.;  of  46  rm. 

25.  Find  the  Cost  of  4600  lb.  of  coal  at  $6.40  per  ton  ($3.20 
per  thousand  pounds)  ;  at  $8.40;  at  $4.60;  at  $6.80  ;  at  $7.20; 
at  $7.40;  at  $9.20;  at  $5.60.  Also  find  the  cost  of  2700  lb. 
at  each  of  the  above  prices ;  of  3900  lb. ;  of  8700  lb. ;  of  9300  lb.; 
of  10,900  lb,;  of  12,800  lb.;  of  13,500  lb.;  of  14,700  1b.;  of 
49,500  1b.;  of  52,500  lb. 

26.  By  the  aid  of  the  table  find  the  total  cost  of : 

525  bolts  at  S1.70  per  C.  128  bolts  at  S1.90  per  C. 

495  bolts  at  S2.40  per  C.  525  bolts  at  S2.70  per  C. 

135  bolts  at  $1.60  per  C.  495  bolts  at  $3.50  per  C. 

27.  By  the  aid  of  the  table  find  the  total  cost  of : 

1280  ft.  lumber  at  $  28  per  M.  5250  ft.  lumber  at  $  27  per  M. 
1350  ft.  lumber  at  $29  per  M.  3800  ft.  lumber  at  $27  per  M. 
4950  ft.  lumber  at  $19  per  M.        4600  ft.  lumber  at  $18  per  M. 

A  REVIEW  EXERCISE 

1.  Without  copying,  extend  and  find  the  total  of  each  invoice 
on  pages  189  and  190.  Time  for  each  invoice,  approximately, 
3  min. 

2.  How  many  acres  in  each  of  the  following  fields : 
a.  A  field  60  rd.  long  and  40  rd.  wide.    ' 

Suggestion.  As  the  field  is  40  rd.  wide,  each  4  rd.  of  length  makes  an  acre ; 
hence,  there  are  as  many  acres  as  4  is  contained  times  in  60.     Ans.  15  A. 

h.  A  field  50  rd.  long  and  32  rd.  wide. 

c.  A  field  80  rd.  long  and  16  rd.  wide. 

d.  A  field  96  rd.  long  and  20  rd.  wide. 

e.  A  field  75  rd.  long  and  531  rd.  wide. 
/.  A  field  80  rd.  long  and  80  rd.  wide. 
g.  A  field  120  rd.  long  and  40  rd.  wide. 


PERCENTAGE   AND    ITS    APPLICATIONS 
CHAPTER  XVII 

PERCENTAGE 
ORAL  EXERCISE 

1.  .50  may  be  read  fifty  hundredths^  one  half  or  fifty  per 
cent.     Read  each  of  the  following  in  three  ways  :   .  25, .  30, 12 J  % . 

2.  Read  each  of  the  following  in  three  ways  :  -J,  J,  \^  ^,  gV' 
h  h  h  h  h  2  %'  H%  125%,  61%.,  81%,  mi%  250%,  375%. 

3.  50  %  of  a  number  is  .50  or  ^  of  the  number.     What  is 
50%  of  1600?    25%?    121%?    10%?    40%?    20%?    75%? 

287.  Per  cent  is  a  common  name  for  hundredths. 

288.  The  symbol  %  may  be  read  hundredths  ov  per  cent. 

289.  Percentage  is  the  process  of  computing  by  hundredths 
or  per  cents. 

ORAL  EXERCISE 

Express  as  per  cerits  : 

1.  .28.         3.    .00^.  5.    .33J.  7.    .621  9.    .5. 

2.  .37.         4.    .14f  6.    .28|.         8.    .0075.      10.    .2. 
Express  as  decimal  fractions  : 

11.  20%.    13.    72%.        15.    1%.         17.    125%.      19.    ^V%- 

12.  45%.    14.    18%.        16.    1%.         18.    250%.     20.    375%. 
Express  as  common  fractions  : 

21.  1%.        23.     2|%.  25.     1331%.    27.     871%.       29.     1%, 

22.  2%.       24.    31%.         26.    26Gf%.   28.    1121%.    30.    175%. 
Express  as  per  cents  : 

31.  1  33.     -^y  35.     !{.  37.    |.  39.     |. 

32.  1  34.     ^^.  36.     2f.  38.    If  40.    ^^K 

231 


232  PRACTICAL  BUSINESS   ARITHMETIC 

Important  Per  Cents  and  their  Fractional  Equivalents 


Per 

Fkaotional 

Per 

Fractional 

Per 

Fractional 

Per 

Fractional 

Cent 

Value 

Cent 

VALUE 

Cent 

Value 

Cent 

Value 

i2r/o 

i 

75% 

1 

831% 

1 

6i% 

h 

25% 

\ 

100% 

1 

20% 

I 

6f% 

iV 

37r/o 

f 

16f% 

I 

40% 

I 

8i% 

1^1 

50% 

1. 

33|% 

\ 

G0% 

f 

1H% 

\ 

62i% 

f 

66f% 

^ 

80% 

f 

in% 

\ 

290.  The  terms  used  in  percentage  are  the  base,  the  rate, 
and  the  percentage.  The  base  is  the  number  of  which  a  per 
cent  is  taken  ;  the  rate,  the  number  of  hundredths  of  the  base 
to  be  taken  ;  the  percentage,  the  result  obtained  by  taking  a 
certain  per  cent  of  the  base. 

In  the  expression  "12  %  of  ^50  is  1 6,"  %  50  is  the  base,  12  %,  the  rate,  and 
$6,  the  percentage. 

291.  The  base  plus  the  percentage  is  sometimes  called  the 
amount  ;  the  base  minus  the  percentage,  the  difference. 

FINDING   THE   PERCENTAGE 


292.    Example.     What  is  15  %  of  %  660  ? 

Solution.     15%  of  a  number  equals  .15  of  it.     .15  of  $660 
%  99,  the  required  result. 


1660 
.15 


199.00 

293.    Obviously,  the  product  of  the  base  and  rate  equals  the 
percentage. 

The  base  may  be  either  concrete  or  abstract.  ^  The  rate  is  always  abstract. 
The  percentage  is  always  of  the  same  name  as  the  base. 

ORAL  EXERCISE 

1.  Whataliquotpartof  lis  .121?    .25?    .50?    .16|  ?   .33J? 
.20?  Ml?  .06|?  .081?  .111?  .142?  371^^?  62-i-%?  66f%? 

2.  Formulate  a  short  method  for  finding  12J%  of  a  number. 
Solution.     12|  %  =  .121  =  i  j  hence,  to  find  12i  %  of  a  number,  divide  by  8. 

3.  State    a  short   method   for   finding   25  %  of   a  number ; 
.3/.;    20%;     61%;    6|%;     81%;    111%. 


50%;     16|%;    331 


PERCENTAGE  233 

To  guard  against  absurd  answers  in  exercises  of  this  character  estimate 
the  results  in  advance  as  explained  on  pages  58  and  146. 

4.  Find   50%    of   960.     Also    25%;  37-1%;  I2i%;  621%; 
75%;  16f%;   331%;   66|%;  831%;  20%;  40%;   60%;   6^%. 

5.  By  inspection  find  : 

a.  50  %  of  1792.  e,  25%  of  S1729.  i.    66f  %  of  2460. 

b.  371%  of  1320.  /.  6f%  of  16600.  j,   331%  of  2793. 

c.  121%  of  $880.-  g,  61%  of  3296.  Jc.   81%  of  24,960. 

d.  16f  %  of  1669.  h.  831%  of  4560..  I   20%  of  12,535. 

ORAL    EXERCISE 

1.  Find  10%  of  720;    of  115.50;    of  120  men;   of  1127.50. 

2.  What  aliquot  part  of  10%  is  5%  ?  21%  ?  li  %  ?  31%  ?  If  %  ? 

3.  Formulate  a  short  method  for  finding  1^  %  of  a  number. 

Solution.     1  J%  of  a  number  is  i  of  10  %  of  the  number  ;  hence,  to  find  1^% 
of  a  number,  point  of  one  place  to  the  left  and  divide  by  8. 

4.  State  a  short  method  for  finding  5  %  of  a  number ;  21  %  ; 

5.  By  inspection  find  : 

a.   5%  of  720.  d.   11%  of  1840.         g.   31%  of  13900. 

h.   21%  of  840.  e.   If  %  of  $366.         h.   1|  %  of  120  mi. 

c.   31%  of  1560.         /.   21%  of  $720.  ^.   IJ  %  of  1632  A. 

ORAL  EXERCISE 

1.  Compare  24%  of  $25  with  25%  of  $24;    24%  of  $2500 
with  25  %  of  $2400.     What  is  32  %  of  $25  ? 

Solution.    32%  of  §  25  =  25%  of  |32  =  ^  of  $32  =  $  8,  the  required  result. 

2.  What  is  125%  of  $880? 

Solution.     125%  =  1.25  =  1  of   10 ;   i  of  $8800  (10  times  $880)  =$1100. 

3.  Find  125%    of  400;  of  640;  of  3200 ;  of  160;  of  1280. 

4.  Formulate  a  short  method  for  finding  166f  %  of  a  num- 
ber ;   3331  %  of  a  number ;   250  %  of  a  number. 

5.  Compare  88  %  of  12,500  bu.  with  125  %  of  8800  bu. 

6.  Find  32%  of  $125;  of  $1250;  of  $12,500;  of  $125,000. 

7.  Find  250%  of  $720;  of  $3200;  of  $28,800;  of  $64,800. 


234  PRACTICAL   BUSINESS   ARITHMETIC 

ORAL  EXERCISE 

By  inspection  find : 

1.   48%  of  250.  5.  180%  of  625. 

•2.   32%  of  125.  6.  160%  of  875. 

3.  128%  of  250.  7.  240%  of  7500. 

4.  16  %  of  2500.  8.  125  %  of  f  240.40. 

WRITTEN  EXERCISE 

1.  A  farmer  sold  640  bu.  wheat,  receiving  f  1.05  per  bushel 
for  87|%  of  it  and  85)^  per  bushel  for  the  remainder.  What 
was  the  total  amount  received  ? 

2.  A  grocer  compromised  with  his  creditors,  paying  60  %  of 
the  amount  of  his  debts.  If  he  owed  A  i  756,  B  »$  1250,  and  C 
$3750,  how  much  did  each  receive  ? 

3.  A  merchant  sold  360  bbl.  apples  for  $1200.  If  he  re- 
ceived $3.50  per  barrel  for  6Q^%  of  the  apples,  what  was  the 
price  received  per  barrel  for  the  remainder  ? 

4.  A  man  bought  a  house  for  $12,864.75;  he  expended  for 
improvements  331  %  of  the  first  cost  of  the  property,  and  then 
sold  it  for  $20,000.     Did  he  gain  or  lose,  and  how  much  ? 

5.  A  commission  merchant  bought  1200  bbl.  apples  and 
after  holding  them  for  3  mo.  found  that  his  loss  from  decay 
was  10%.  If  he  sold  the  remainder  at  $3.75  per  barrel,  how 
much  did  he  receive  ? 

6.  A  merchant  prepaid  the  following  bills  and  received  the 
per  cents  of  discount  named:  4%  on  bill  of  $875.50;  6%  on 
bill  of  $378.45;  2%  on  bill  of  $940.50;  3|  %  on  bill  of  $400. 
What  was  the  net  amount  paid  ? 

FINDING   THE   RATE 
ORAL  EXERCISE 

1.  8  is  what  part  of  40  ?  what  per  cent  of  40  ? 

2.  90  is  what  per  cent  of  270  ?  of  360  ?  of  450  ? 

3.  70  is  what  per  cent  of  560?  of  630  ?  of  700  ? 

4.  The  base  is  900  and  the  percentage  450 ;  what  is  the  rate  ? 


PEECENTAGE  235 

294.  Example.    $35.50  is  what  per  cent  of  8284  ? 

Solutions,     a.   $35.50  is  ^^^^.o^  or  \  of  {a) 

$284.     $284   is  100%  of   itself;    hence,  _3_55JL  _.  i  _  J^21  ^ 

$85.50,  which  is  \  of  $284,  must  be  ^  of  2  810  0        8            2  / 

100%,  or  121%.     Or,  Q>) 

h.   Since  the  product  of  the  base  and  __J^5  =  12^ffo 

the  rate  is  the  percentage,  the  quotient  284)35.50 
obtained  by  dividing  the  percentage  by  the  base  is  the  rate. 

295.  Obviously,  the  percentage  divided  hy  the  base  equals  the 

rate. 

ORAL  EXERCISE 

What  per  cent  of: 

1.  95  is  19?                      -  7.  1.6  is  .008? 

2.  4.8  is  1.2?  8.  1yd.  is  1ft.  ? 

3.  $35  is  1171  ?  9.  2  da.  are  8  hr.  ? 

4.  225  A.  are  75  A.  ?  lo.  4  T.  are  3000  lb.  ? 

5.  34  bu.  are  34  bu.  ?  ii.  1  yr.  are  4  mo.  ? 

6.  34  bu.  are  68  bu.  ?  12.  2  mi.  are  80  rd.  ? 

WRITTEN  EXERCISE 

1.  A  man  bought  a  house  for  §7500  and  sold  it  for  18700. 
What  per  cent  did  he  gain  ? 

2.  In  a  certain  city,  school  was  in  session  190  da.  A  lost  38 
da.     What  per  cent  of  the  school  year  did  he  attend? 

3.  An  agent  sold  a  piece  of  property  for  $8462.50  and  re- 
ceived $338.50  for  his  services.  What  per  cent  did  he 
receive  ? 

4.  A  commission  agent  sold  28,600  bu.  of  grain  at  50  ^  per 
bushel  and  received  for  his  services  $357.50.  What  per  cent 
did  he  receive  on  the  sales  made  ? 

5.  Smith  and  Brown  engaged  in  business,  investing  $18,000. 
Smith  invested  $10,440,  and  Brown  the  remainder.  What  per 
cent  of  the  total  capital  did  each  invest  ? 

6.  An  agent  for  a  wholesale  house  earned  $165.55  during 
the  month  of  May.  If  the  goods  sold  amounted  to  $  1505,  what 
per  cent  did  he  receive  on  the  sales  made  ? 


236  PEACTICAL   BUSINESS  ARITHMETIC 

FINDING   THE   BASE 

ORAL  EXERCISE 

1.  What  is  5%  of  240  bu.  ? 

2.  12  bu.  is  5  %  of  how  many  bushels  ? 

3.  160  is8%  of  what  number  ?  4%?  2%?1%?|%?  i%? 

4.  The  multiplicand  is  400  and  the  multiplier  10;  what  is 
the  product?  The  product  is  2000  and  the  multiplicand  100; 
what  is  the  multiplier?  The  product  is  4000  and  the  multi- 
plier 20  ;    what  is  the  multiplicand  ? 

5.  In  percentage  what  name  is  given  to  the  product  ?  to 
the  multiplicand  ?  to  the  multiplier  ?  When  the  base  and  rate 
are  given,  how  is  the  percentage  found  ?  When  the  percentage 
and  base  are  given,  how  is  the  rate  found  ?  When  the  per- 
centage and  rate  are  given,  how  is  the  base  found  ? 

296.  Example.    37.5  is  25%  of  what  number? 

Solution.     25%  or  I  of  the  number  =  37.5 
.  •.  the  number  =  37.5  -^  ^  =  150. 

297.  Obviously,  the  quotient  of  the  percentage  divided  hy  the 
rate  equals  the  base. 

WRITTEN  EXERCISE 

1.  N  invested  30%  of  the  capital  of  a  firm,  H  35%,  and  W 
the  remainder,  $1400.     What  was  the  capital  of  the  firm? 

2.  During  the  month  of  May  the  sales  of  a  clothing  mer- 
chant amounted  to  $4864.24,  which  was  8  %  of  the  total  sales 
for  the  year.    What  were  the  total  sales  for  the  year? 

3.  B  sold  his  city  property  and  took  a  mortgage  for  $4375, 
which  was  1TJ%  of  the  value  of  the  property.  If  the  balance 
was  paid  in  «ash,  what  was  the  amount  of  cash  received  ? 

4.  In  compromising  with  his  creditors,  a  man  finds  that  his 
assets  are  1270,900,  and  that  this  sum  is  43%  of  his  entire  in- 
debtedness.     What  will  be  the  aggregate  loss  to  his  creditors? 

5.  The  aggregate  attendance  in  the  schools  of  a  certain  city 
for  1  da.  was  43,225  students.  If  this  number  was  95%  of  the 
number  of  students  belonging,  how  many  students  were  absent? 


PERCENTAGE  237 

PER  CENTS  OF  INCREASE 

ORAL  EXERCISE 

1.  If  2|  times  a  number  is  50,  what  is  the  number? 

2.  If  2.5  times  a  number  is  75,  what  is  the  number? 

3.  If  250%  of  a  number  is  $1250,  what  is  the  number? 

4.  If  250%  of  a  number  is  150,  what  is  the  number?  If 
250%  is  125,  what  is  the  number? 

5.  If  300%  of  a  number  is  $5400,  what  is  the  number? 

298.  Examples,  i.  A  man  sold  a  farm  for  $3900  and 
thereby  gained  30%.     How  much  did  the  farm  cost? 

Solution.     1.30  of  the  cost  =  $3900. 

.  • .  the  cost  =  $  3900  -T- 1 .30  =  $  3000. 

2.    What  number  increased  by  33^%  of  itself  equals  180? 

Solution.     |  of  the  number  =  180. 

.  •.  the  number  =  180  h-  |  =  135. 

ORAL  EXERCISE 

What  number  increased  by: 

1.  10%  of  itself  is  220?  8.  6f  %  of  itself  is  480? 

2.  25%  of  itself  is  125?  9.  125%  of  itself  is  900? 

3.  50%  of  itself  is  300?  10.  37^%  of  itself  is  440? 

4.  75%  of  itself  is  700?    '  li.  11^%  of  itself  is  300? 
.5.  6|%  of  itself  is  170?  12.  14f  %  of  itself  is  328? 

6.  121%  of  itself  is  180?  .  13.  200%  of  itself  is  2700? 

7.  661%  of  itself  is  135?  14.  300%  of  itself  is  2800? 

WRITTEN  EXERCISE 

1.  I  sold  375  bu.  of  wheat  for  $427.50,  thereby  gaining  20%. 
How  much  did  the  wheat  cost  me  per  bushel? 

2.  A  fruit  dealer  sold  a  quantity  of  oranges  for  $6.75.  If 
his  gain  was  121%,  what  did  the  oranges  cost  him? 

3.  My  savings  for  March  increased  33^%  over  February.  If 
my  savings  for  March  were  $84.36,  what  were  my  savings  for 
February  and  March? 


238  PEACTICAL   BUSINESS   AKITHMETIC 

PER   CENTS   OF   DECREASE 

ORAL   EXERCISE 

1.  What  per  cent  of  a  number  is  left  after  taking  away 
331%   of  it  ?     What  fractional  part? 

2.  If  I  of  a  number  is  600,  what  is  the  number  ?  If  G6|  %  of 
a  number  is  75,  what  is  the  number  ? 

3.  A  man  spent  40  %  of  his  money  and  had  $60  remaining. 
How  much  had  he  at  first  ?    How  much  did  he  spend? 

299.  Examples,  l.  A  man  sold  a  horse  for  $332,  thereby 
losing  17  %.     What  was  the  cost  ? 

Solution.     0.83  of  the  cost  =  $332. 

.  •.  the  cost  =  f  332  --  0.83  =  $  400.  • 

2.    What  number  decreased  by  25  %  of  itself  equals  $375? 

Solution.     |  of  the  number  =  $  375. 

.  •.  the  number  =  $  375  -=-  f  =  $  500. 

ORAL  EXERCISE 

What  number  diminished  hy: 

1.  61  %  of  itself  equals  75  ?  4.-1  of  itself  equals  750  ? 

2.  81%  of  itself  equals  440?  5.    1%  of  itself  equals  99.5? 

3.  6|%  of  itself  equals  280?  6.   1%  of  itself  equals  49.5? 

WRITTEN   EXERCISE 

1.  Of  what  number  is  9581.88   77  %  ? 

2.  A  merchant  sold  1200  bu.  of  potatoes  for  $640,  which 
was  16|%  less  than  he  paid  for  them.  What  was  the  cost  per 
bushel? 

3.  In  selling  a  carriage  for  f  75  a  merchant  lost  25%  on  the 
cost.  What  was  the  asking  price  if  the  carriage  was  marked 
to  gain  25  %  ? 

4.  A  newsboy  sold  92  papers  on  Tuesday.  If  this  number 
was  23J%  less  than  the  number  sold  on  Monday,  how  many 
papers  were  sold  on  the  two  days  ? 

5.  A  dealer  sold  a  quantity  of  apples  at  $6  per  barrel,  and 
by  so  doing  lost  16|%.  If  he  paid  $309.60  for  the  apples, 
how  many  barrels  did  he  buy  ? 


PEECENTAGE 


239 


ORAL  REVIEW  EXERCISE 


1.  By  inspection  find  12| 
a.  ^872.  e.  12464. 
h.  648  bu.          /.  2696  A. 

c.  1264  A.  g.  1624  ft. 

d.  960  mi.  h.  1832  mi. 

2.  By  inspection  find  10 
25%  ;  125%  ;  20%. 


of  the  following  numbers  : 

i,  11688.  m.  I24.T2. 

j.  2072  A.  7u   1168.48. 

h,  11,464  mi.        0.    $176.24. 
I.   37,128  mi.       p.  12184.32. 
of  each  of  the  above  numbers  : 


3.    State  the  missing  term  in  each  of  the  following : 


No. 

Base 

Kate 

Percentage 

■■  No. 

Base 

Rate 

Percentage 

a. 

$600 

7^% 

v 

/. 

906 

16f% 

? 

h. 

§650 

? 

^  ;39 

9- 

? 

8i% 

15  bu. 

c. 

? 

4% 

$1^ 

h. 

1275 

61% 

? 

d. 

900 

? 

720 

i. 

? 

6|-% 

21  mi.     \ 

e. 

? 

4% 

20 

J- 

400 

? 

600 

\\' 


4.  By  inspection  find  10  ^ 

a.  8264.  d.  1840. 

h.   1920.  e.    1750. 

(?.   1720.  /.  $364. 

5.  By  inspection  find  1-| 


^  of  each  of  the  following  : 

ff.  1232.  y.  12448. 

^.  1144.  h  11432. 

z.  $288.  L   $3624. 

%  of  each  of  the  above  numbers ; 


1|%;   1000%;   125%;   166f%. 

WRITTEN  REVIEW  EXERCISE 

1.  A  collector  charged  4  %  on  all  amounts  collected.  If  he 
remitted  to  his  customers  in  one  month  $3720.48,  how  much 
did  he  receive  for  his  services? 

2.  A  father  left  to  his  son  60  %  of  his  estate  and  to  his 
daughter  the  remainder,  $9390.88.  What  was  the  value  of  the 
estate  and  how  much  did  the  son  receive? 

3.  A  farmer  planted  Wbrrr-fe'pk.  of  oats  on  an  acre  of  ground 
and  harvested  56  bu.  What  per  cent  of  the  yield  was  the 
planting?     What  per  cent  of  the  planting  was  the  yield? 

4.  A  merchant  paid  the  following  charges  on  a  bill  of  goods  : 
cartage  $12.45,  freight  $65.32,  insurance  $41.  If  the  charges 
represent  5  %  of  the  face  of  the  bill,  what  was  the  gross  cost  of 
the  goods? 


240  PRACTICAL   BUSINESS  ARITHMETIC 

5.  A  man  had  6  Ai^  of  land;  to  one  party  he  sold  a  piece 
25  rd.  by  20  rd.,  and  to  another  party  140  sq.  rd.  What  per 
cent  of  the  field  remained  unsold? 

6.  In  a  recent  year  191,571,750  lb.  of  fish  were  landed  in 
Boston  and  Gloucester,  and  of  this  quantity  103,460,410  lb. 
were  landed  in  Gloucester  and  88,111,340  in  Boston.  What 
per  cent  of  the  total  was  furnished  by  each  city  ?  (Correct 
to  the  nearest  .01.) 

7.  A  owned  property  valued  at  $12,000  from  which  he 
received  a  yearly  rental  of  S960.  If  he  paid  taxes  amounting 
to  $160,  insurance  $75.50,  and  made  repairs  amounting  to 
$184.50,  what  per  cent  net  income  did  he  receive? 

8.  B  owns  a  field  80  rd.  square.  During  a  certain  year 
this  field  yielded  on  an  average  25  bu.  of  wheat  to  an  acre. 
The  wheat  when  sold  at  $1  a  bushel  produced  an  amount  equal 
to  25  %  of  the  value  of  the  field.  What  was  the  value  of  the 
field  ? 

.  9.  A  landowner  rented  a  field  to  a  tenant  and  was  to 
receive  as  rent  16|%  of  the  grain  raised.  The  owner  of  the 
field  sold  his  share  of  the  grain  for  84/  per  bushel,  receiving 
$298.20.  If  the,  tenant  sold  his  share  of  the  grain  for  the  same 
price  per  bushel,  how  much  did  he  receive  ? 

10.  In  a  single  year  the  cost  of  the  cotton  yarn  used  in  the 
manufacture  of  hosiery  and  knit  goods  in  the  state  of  New  York, 
in  round  numbers,  was  $13,825,000;  in  the  state  of  Illinois, 
$1,550,000.  The  cost  of  the  cotton  yarn  used  in  Illinois  was 
what  per  cent  less  than  the  cost  of  the  cotton  yarn  used  in 
New  York,  in  a  year?  (Correct  to  the  nearest  .01.) 
-  11.  By  a  recent  census  report  it  was  shown  that  the  value 
of  all  personal  property  in  the  state  of  New  York  was 
approximately  $500,000,000  and  the  value  of  all  the  real  estate 
approximately  $10,000,000,000.  Draw  parallel  lines  making 
a  comparison  of  the  personal  property  and  the  real  estate.  The 
real  estate  is  what  per  cent  greater  than  the  personal  property  ? 
The  personal  property  is  what  per  cent  less  than  the  real 
estate  ? 


PERCENTAGE  241 

12.  A  young  man  entered  a  bank  as  cashier  and  at  the  end- 
of  the  first  year  his  salary  was  increased  25%  ;.at  the  end  of 
the  second  year  he  was  given  an  increase  of  20  %  ;  and  at  the 
end  of  the  third  year  he  was  given  an  increase  of  25%,  which 
made  his  salary  f  4500.     What  salary  did  he  receive  at  first  ? 

13.  A  government  statistician  collected  facts  regarding  wages 
and  income  from  nearly  two  thousand  private  manufacturing 
concerns,  and  reported  the  following :  the  average  wages  of  all 
employees,  men,  women,  and  children,  per  year  was  $  263.06,  and 
the  average  net  profit  for  each  employer  was  $  2273.  What  per 
cent  greater  was  the  income  of  each  employer  than  of  each  em- 
ployee ?     (Correct  to  the  nearest  .01.) 

2     14.   The  population  of  three 


1 1 1  h  M 1 1 1 1 1 1 1 1 1'l  1 1 1 1 1 1 1 1  iTtm- 


cities  during  a  certain  year  is 
At^^ma^^^^t^^mma^m^^  illustrated  by  the  accompany- 
Bm^^mt^m^^mK^m^^m  ing  lines,  which  are  drawn  on 

ciMHBiiH^HaMMHii  a  scale  of  12,500  inhabitants 

to  each  -|  of  an  inch.  What  is  the  population  of  A,  B,  and  C, 
respectively  ?  The  population  of  each  city  is  what  per  cent  of 
the  population  of  the  three  cities  ? 

15.    The  annual  coal  production  in  the  United  States,  Great 
Britain,  Germany,  and  France 


for  a  certain  year  is  illustrated  h  I  i  1 1  1 1  I  i  1 1  I  1 1 1  h  1 1 1 1 1  1 1 1 1 1  I  1 1  i 


in  the  accompanying  rectan-  United  states 

gles,  drawn   on  the  scale    of 
50,000,000  short  tons  to  each  £SiSlSilM 
^  of  an  inch.      During  that  oermaiy^ 
year,  how  many  tons    did  the  jYanoe 
United  States,  Great  Britain,  "• 

Germany,  and  France,  respectively,  produce?  The  produc- 
tion of  each  country  is  what  per  cent  of  the  production  of  the 
four  countries  ?  In  the  same  ,year  the  rest  of  the  world  pro- 
duced approximately  200,000,000  short  tons.  Illustrate  graph- 
ically the  world's  coal  production  for  that  year.  What  was  the 
world's  approximate  production  this  year  ? 


242  PEACTICAL   BUSINESS  AEITHMETIC      * 

16.  The  total  value  of  the  cotton  crop  to  farmers  in  a  recent 
year  was  S 920,630,000  and  the  value  of  the  cotton  exported  to 
Great  Britain  in  the  same  year  was  $  231,817,000.  What  per  cent 
was  exported  to  Great  Britain?     (Correct  to  the  nearest  .01.) 

17.  A  saleswoman  in  a  city  store  receives  $9  per  week.  She 
pays  S3.50  per  week  for  board  and  room,  10/ per  day  for  car 
fare  6  da.  of  the  week,  20/  per  day  for  6  da.  of  each  week 
for  luncheon,  and  has  incidental  expenses  amounting  to  S1.70. 
If  she  saves  the  remainder,  what  per  cent  of  her  weekly  wages 
does  she  save  ?    What  per  cent  does  she  spend  ?         j 

18.  The  production,  in  bushels,  of  grain  in  the  Uiiited  States 
in  two  recent  years  was  approximately  as  follows : 


Cereals 

1912 

1913 

Corn 

3,124,000,000 

2,370,000,000 

Wheat 

730,000,000 

753,000,000 

Oats 

1,418,000,000 

1,122,000,000 

Barley 

223,000,000 

175,000,000 

Rye 

35,000,000 

34,000,000 

Buckwheat 

19,000,000 

14,000,000 

Find  the  per  cent  of  increase  or  decrease  of  each  cereal  for 
1913  as  compared  with  the  previous  year.  Then  draw  a  series  of 
parallel  rectangles  to  compare  the  production  of  1913  with  the 
production  of  1912.  Also  draw  a  series  of  rectangles  to  com- 
pare the  production  of  1913  with  the  production  of  a  later  year. 

Suggestion.  This  may  be  represented  by  one  series  of  rectangles. 
Each  rectangle  may  be  divided,  into  two  parts  —  one  shaded  and  the  other 
unshaded.  The  shaded  part  may  be  made  to  represent  the  yield  for  1913 
and  the  unshaded  part  the  yield  for  1912. 

19.  The  silver  produced  by  the  leading  sources  in  a  recent 
year  was  approximately  as  follows : 

32,000,000  oz. 

6,000,000  oz. 

4,000,000  oz. 

4,500,000  oz. 

Austria-Hungary    1,500,000  oz. 

Draw  a  set  of  parallel  rectangles  to  represent  graphically  the 
above  numbers. 


Mexico 

80,000,000  oz. 

Canada 

United  States 

60,000,000  oz. 

Peru 

Turkey 

1,500,000  oz. 

Spain 

Australia 

16,000,000  oz. 

Japan 

Germany 

6,000,000  oz. 

Austria 

PERCENTAGE 


243 


20.  In  the  following  table  is  shown  the  population  in  the 
United  States  in  a  certain  year,  men  and  women,  engaged  in 
gainful  occupations,  classified  according  to  geographic  divisions. 
Supply  the  missing  terms.     Check  the  work. 


Engaged  in  Gainful  Occupations 

Geogkaphic  Divisions 

Number 

Per  Cent  of  Total 

Total 

Men 

Women 

Total 

Men 

Women 

North  Atlantic     .     .     . 
South  Atlantic     .     .     . 
North  Central      .     .     . 
South  Central      .     .     . 
Western 

8,274,869 
3,553,985 
9,211,119 
4,610,924 
1,672,158 

6,539,941 
2,781,825 
7,895,395 
3,792,422 
1,479,842 

1,734,928 
772,160 

1,315,724 
818,502 
192,316 

30.3 
? 

? 
? 
? 

29.1 

9 
9 
9 
9 

35.9 

■    ? 

? 

? 

? 

Totals 

? 

? 

? 

100.0 

100.0 

100.0 

Public 


21.  Suppose  the  accompanying  diagram  illustrates  the  distri- 
bution of  school  enrollment  in  the  public,  private,  and  parochial 
schools  of  the  United  States  during 
a  certain  year.  The  private  and 
parochial  schools  are  what  per  cent 
of  the  public  schools?  of  the  en- 
tire school  enrollment  ?  The  public 
schools  are  what  per  cent  of  the 
total  enrollment  ?  of  the  private  and 
parochial  schools  combined  ? 

22.  The  gold  production  in  the 
eight  principal  gold-producing  states 
in  the  United  States  in  a  recent 
as  follows:  Colorado,  900,000  oz. 
Arizona,  180,000  oz. ;  Montana,  170,000  oz. ;  Nevada,  800,000 
oz. ;  South  Dakota,  350,000  oz. ;  Utah,  200,000  oz. ;  Idaho, 
60,000  oz.  Compare  these  values  by  drawing  a  series  of 
parallel  rectangles. 


Parochial 


Private 


year    was    approximately 
California,   960,000   oz. ; 


244  PEACTICAL  BUSINESS  ARITHMETIC 


A   REVIEW  EXERCISE 

Illustrate  the  following  problems  by  the  use  of  graphs.  Graph  forms  are 
given  on  pages  144,  153,  243.     Use  the  form  suggested  by  the  instructor. 

1.  Illustrate  graphically  problem  3,  page  85.  Use  the  even 
number  of  thousands  for  each  month. 

2.  In  a  recent  year  the  railway  mileage,  single-track,  of  the 
world  was  as  follows :  America,  325,000  mi. ;  Europe,  200,000  mi. ; 
Asia,  63,000  mi. ;  Africa,  23,000  mi. ;  Austraha,  19,000  mi.  Illus- 
trate graphically,  showing  the  total  mileage,  and  the  relation 
that  each  country  bears  to  the  total. 

3.  In  a  recent  year  there  were  enrolled  in  the  schools  and  col- 
leges of  the  United  States  20,000,000  students,  grouped  accord- 
ing to  ages  as  follows:  5  yr.,  400,000;  6  to  9  yr.,  6,200,000; 
10  to  14  yr.,  9,000,000;  15  to  17  yr.,  3,000,000;  18  to  20  yr., 
1,000,000  ;  21  to  24  yr.,  400,000.  Illustrate  graphically.  Each 
group  is  what  per  cent  of  the  total  ? 

4.  The  number  of  cattle,  other  than  milch  cows,  on  farms  and 
ranches  in  the  United  States,  as  reported  by  the  decennial  cen- 
suses, for  the  years  named  were  as  follows:  1870,  13,500,000; 
1880,  22,500,000;  1890,  33,500,000;  1900,  50,000,000;  1910, 
41,000,000.  Illustrate  graphically.  What  do  these  figures  sug- 
gest regarding  the  cost  of  living  as  applied  to  beef  ? 

5.  The  following  figures  represent  the  latest  estimates  of  the 
wealth  of  the  nations  named.  The  figures  given  represent  bil- 
lions of  dollars:  United  States,  130;  Great  Britain  and  Ireland, 
80;  France,  65;  Germany,  60;  Russia,  40;  Austria-Hungary,  25; 
Italy,  20;  Belgium,  9;  Spain,  5i;  Netherlands,  5;  Portugal,  2|-. 
Switzerland,  21.     Illustrate  graphically. 

6.  In  a  recent  year  the  cities  of  the  United  States  which 
had  a  population  of  over  100,000  expended  $100,000,000  in 
various  school  expenses,  according  to  the  following  geographical 
divisions:  North  Atlantic  Division,  $54,000,000;  North  Cen- 
tral Division,  $30,000,000;  South  Atlantic  Division,  $2,700,- 
000;  South  Central  Division,  $3,000,000;  Western  Division, 
$10,300,000.     Illustrate  graphically. 


PERCENTAGE  245 

A  WRITTEN  REVIEW  TEST 

(Time,  approximately,  forty  minutes) 

1.  A  gardener  planted  1  qt.  of  corn  and  harvested  5  bu.  What 
per  cent  of  the  planting  was  the  harvest  ? 

2.  A  bookkeeper  made  an  investment  on  which  he  lost  15%. 
If  the  sum  returned  to  him  was  S  1912.50,  what  was  the 
investment  ? 

3.  A  piece  of  cloth,  unfinished,  cost  6/  per  yard.  It  costs 
.0075/  per  yard  to  bleach  it,  and  then  it  sells  for  7|/  per  yard. 
The  selling  price  is  what  per  cent  advance  over  the  total  cost  ? 

4.  A  merchant  paid  the  following  bills  less  the  discounts 
named:  S85.50  less  2%  ;  S141.50  less  3%  ;  $117.95  less  1%  ; 
S225.40  less  li%  ;  S47.50  less  2i%.  What  was  the  total  sum 
paid  ?  .  What  was  the  total  discount  allowed  ? 

5.  On  Monday  a  man  deposited  in  the  bank  S  184.96.  On 
Wednesday  he  deposited  a  sum  12|  %  greater  than  the  deposit 
of  Monday ;  he  then  drew  a  check  for  50  %  of  his  total  deposit. 
What  was  the  amount  of  the  check  ? 

6.  A  merchant's  sales  mcreased  the  second  month  of  his 
business  25%  over  the  first  naonth;  the  third  month  they  in- 
creased 20%  over  the  second  month;  the  fourth  month  they 
decreased  10%  from  the  sales  of  the  third  month.  What  were 
the  sales  for  each  month  if  they  were  S  3240  for  the  fourth  month  ? 

7.  A  farmer  used  1200  lb.  of  potato  fertilizer  per  acre,  on  a 
16-acre  field  of  potatoes.  The  fertilizer  cost  $24,125  per  ton, 
less  5%  for  cash  payment.  If  the  unfertilized  land  produced 
60  bu.  of  potatoes  per  acre,  and  the  fertilized  land  produced 
150  bu.  per  acre,  what  per  cent  of  increase  was  realized  by 
using  the  fertilizer  if  the  potatoes  sold  for  80/  per  bushel? 

8.  A  man  bought  a  piece  of  land,  and  at  the  end  of  the  first 
year  it  had  increased  in  value  25%  ;  at  the  end  of  the  second 
year  it  had  increased  an  additional  8  %  in  value ;  at  the  end  of 
the  third  year  it  had  increased  an  additional  5%  in  value. 
What  did  he  pay  for  the  property  if  at  the  end  of  the  third 
year  it  was  worth  $2551.50? 


CHAPTER   XYIII 

COMMERCIAL  DISCOUNTS 
ORAL  EXERCISE 

1.  A  set  of  Scott's  works  is  marked  $12.  If  I  buy  it  at  this 
price,  less  16|%,  what  does  it  cost  me? 

2.  I  buy  $90  worth  of  goods  on  30  da.  time,  or  5%  off  for 
cash.     What  cash  payment  will  settle  the  bill  ? 

3.  I  owe  B  $600,  due  in  30  da.  He  offers  to  allow  me  5% 
discount  if  I  pay  cash  to-day.  I  accept  his  offer  and  give  him 
a  check  for  the  amount.     What  was  the  amount  of  the  check  ? 

300.  A  reduction  from  the  catalogue  (list)  price  of  an  article, 
from  the  amount  of  a  bill  of  merchandise,  or  from  the  amount 
of  a  debt,  is  called  a  commercial  or  trade  discount. 

Business  houses  usually  announce  their  terms  upon  their  bill  heads.  The 
space  allowed  for  recording  the  terms  is  usually  limited,  and  bookkeepers 
find  it  necessary  to  use  symbols  and  abbreviations  to  indicate  them.  Thus, 
if  a  bill  is  due  in  30  da.  without  discount,  the  terms  may  be  written 
^/soj  or  Net  30  da. ;  if  the  bill  is  due  in  30  da.  without  discount,  but  an 
allowance  of  2%  is  made  for  payment  within  10  da.,  the  terms  may  be 
written  ^/jq,  ^/^,  or  2  %  10  da.,  net  30  da. 

301.  Manufacturers,  jobbers,  and  wholesale  dealers  usually 
have  printed  price  lists  for  their  goods.  To  obviate  the  neces- 
sity of  issuing  a  new  catalogue  every  time  the  market  changes, 
these  lists  are  frequently  printed  higher  than  the  actual  selling 
price  of  the  goods,  and  made  subject  to  a  trade  discount. 

302.  The  fluctuations  of  the  market  and  the  differences  in 
the  quantities  purchased  by  different  customers  frequently  give 
rise  to  two  or  more  discounts  called  a  discount  series. 

Large  purchasers  sometimes  get  better  prices  and  terms  than  small  pur- 
chasers. Thus,  the  average  customer  might  be  quoted  the  regular  prices 
less  a  trade  discount  of  25  %,  while  an  especially  large  buyer  might  be  quoted 
the  regular  prices  less  trade  discounts  of  25  %  and  10  %. 

246 


COMMERCIAL   DISCOUNTS  247 

303.  When  two  or  more  discounts  are  quoted,  one  denotes  a 
discount  oil  the  list  price,  another,  a  discount  off  the  remainder, 
and  so  on. 

The  order  in  which  the  discounts  of  any  series  is  considered  is  not 
material.  Thus,  a  series  of  25  %,  20  %,  and  10  %  is  the  same  as  one  of  20  %, 
10  %,  and  25  %,  or  one  of  10  %,  25  %,  and  20  %. 

304.  Catalogue  prices  are  generally  estimated  on  the  basis  of 
credit  sales,  and  a  cash  purchaser  is  given  the  usual  trade  dis- 
count and  a  special  discount  for  early  payment.  This  latter 
discount  has  the  effect  of  encouraging  prompt  payments. 

The  list  price  is  sometimes  called  the  gross  price  and  the  price  after  the 
discount  has  been  deducted  the  net  price. 

FINDING   THE   NET   PRICE 

305.  Example.  The  list  price  of  a  dozen  pairs  of  shoes  is 
$45.  If  this  price  is  subject  to  a  discount  series  of  20%  and 
10%,  what  is  the  net  selling  price? 

Solution.    20%  or  ^  of  $45  =  $9,  the  first  discount. 

$45  —  $9  =  $36,  the  price  after  the  first  discount 
10%  or  j\  of  $36  =  $3.60,  the  second  discount. 
$36  -  $3.60  =  $32.40,  the  net  selling  price. 

ORAL  EXERCISE 
Find  the  net  price  :. 

List  Trade  List        Trade  List  Trade 

Price      Discount  Price     Discount  Price  Discounts 

1.  14  25%  8.  $Q  40%  15.  $4  25%    and  331% 

2.  fl5  20%  9.  $4  12|%  16.  130  331%  and  25% 

3.  190  331%  10.  $24  81%  17.  $35  20%    and  25% 

4.  120  10%  11.  142  16|%  18.  $45  20%     and  16| 


7o 


5.  $50      50%       12.  $35     20%       19.   $50    20%     and  25% 

6.  $2.50  20%       13.   $100  25%       20.   $100  20%     and  10% 

7.  $4.50  16f%     14.   $720  331%     21.   $600  16§%  and  20% 

22.  A  piano  listed  at  $750  is  sold  less  331  %,  20  %,  and  10  %. 
What  is  the  net  cost  to  the  purchaser  ? 

23.  A  dealer  offers  cloth  at  $3.50  per  yard  subject  to  a  dis- 
count of  20  %.     How  many  yards  can  be  bought  for  $5Q  ? 


248 


PRACTICAL  BUSINESS  AKITHMETIC 


WRITTEN  EXERCISE 

Find  the  net  price : 

Gross 
Selling  Price  Trade  Discounts 

1.  13360     25%  and  10% 

2.  $3510     331%  and  20% 

3.  14500     20%  andl6f% 


Gross 
Selling  Price  Trade  Discounts 

4.  12500     20%,  10%,  and  5% 

5.  15400     25  %,  20  %,  and  10  % 

6.  13960     331%,  20%,andl6|% 

7.  The  list  price  of  cloth  is  14.80  per  yard,  but  this  price  is 
subject  to  discounts  of  25%  and  20%.  How  many  yards  can 
bebought  for  1288? 

8.  A  hardware  dealer  sold  25  doz.  5-in.  files  at  12.50  and 
25  doz.  12-in.  files  at  17.50,  less  50%  and  10%;  150  machine 
bolts  at  $21.50  per  C,  less  20%  and  10%.  What  was  the  net 
amount  of  the  bill  ? 

9.  Study  the  following  model.  Copy  and  find  the  net 
amount  of  the  bill,  using  the  discounts  named  in  the  bill,  and 
the  following  prices  :  5-in.  pipe,  f  1.45  ;  1-in.  pipe,  17^  ;  valves, 
$2.67. 


M.^^-L 


^^^^.^?^  .<^^. 


Chicago,  111.. yU^^^  /  ^  tg 


Z2^f:^^ 


-^^^^^  CQ. 


Bought  of  GEORGE  W.  MUNSON  &  CO. 


Terms. 


^^77,  ^  ^j:^^>7^^^^^^?-7^'^:^^ 


6£A^. 


L2JL 


JC /^r-7^^. 


/A^^IA^ 


r?^< 


^£J2- 


^^  j-<pV. 


2^ 


Z2J.. 


c^^^ 


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zz 


j^ 


z^^^^. 


(/^-^. 


t^a  2^.^ 


J^ 


^XV'^ 


J^ 


^^.<£^  Z-^'/. 


JC 


^^^^/4^4Y^ 


j^ 


2JJ.^^ 


COMMERCIAL  DISCOUNTS  249 

10.  One  firm  offers  a  piano  for  $400,  subject  to  discounts  of 
20%  and  20%  ;  another  offers  the  same  piano  for  $400  less 
discounts  of  25 %  and  15%.  Which  is  the  better  offer?  How 
much  better? 

11.  A  jobber  bought  a  quantity  of  goods  listed  at  1 3600,  sub- 
ject to  discounts  of  25%  and  20  %.  He  sold  the  goods  at  the 
same  list  price,  subject  to  discounts  of  20  %  and  10  %.  Did  he 
gain  or  lose,  and  how  much? 

12.  Make  out  bills  for  the  following,  using  the  current  date 
and  the  name  and  address,  of  some  dealer  whom  you  know. 
Terms  in  each  case,  60  da.  net. 

a.  You  bought  12  doz.  hand  saws,  #27,  at  $18.50;  "l\  doz. 
mortise  locks,  #271,  at  $4.25;  25  doz.  pocket  knives,  #27,  at 
$7.50;  and  If  doz.  cheese  knives  at  $8.25.    Discount:  25^,10^. 

h.  You  bought  41  J'  of  2^'  extra  strong  iron  pipe  at  70^; 
94i'  of  11"  extra  strong  iron  pipe  at  31 J^;  153J^  of  \^  iron 
pipe  at  6|^;  88^'  of  f '  iron  pipe  at  7|^.     Discount:  25^,  10^. 

c.  You  bought  25  kitchen  tables  at  $3.25;  25  dining-room 
tables  at  $8.75;  15  doz.  dining-room  chairs  at  $12.50;  12 
antique  rockers  at  $12.25;  and  15  oak  bedroom  sets  at  $32.50. 
Discount:  16|%,  5%. 


FINDING  A  SINGLE  KATE  OE  DISCOUNT  EQUIVALENT 
TO   A   DISCOUNT   SERIES 

306.    Example.    What  single  rate  of  discount  is  equivalent 
to  a  discount  series  of  25  %,  33^%,  and  10%  ? 

Solution.    Represent   the   list  price   by  1.00 

100%.    Then,  75%  equals  the  price  after  the  .25  (25%  of  100  %) 

first  discount,  60%  the  price  after  the  second  „r 

discount,  and  45%  equals  the  net  selling  price.  *     . 

100  %,  the  list  price,  minus  45  %,  the  net  selling  _^  (331  %  of  75  %  ) 

price,  equals  55%,  the  single  rate  of  discount  .50 


equivalent  to  the  given  discount  series.  05  TIO  ^7    of  50  ^  ^ 

A  single  discount  equivalent  to  a  discount  — rp 
series  may  often  be  determined  mentally  (see 

§§  307-308).  100  %  -  45  %  =  bb  % 


250  PEACTICAL   BUSINESS   ARITHMETIC 

WRITTEN  EXERCISE 

•  7u.    Find  a  single  rate  of  discount  equivalent  to  a  discount 
series  of  50%,  25%,  20%,  and  10%. 

2.  Which  is  the  better  for  the  buyer  and  how  much,  a  single 
discount  of  6b  %  or  a  discount  series  of  25  %,  20  %,  and  20  %? 

3.  The  net  amount  of  a  bill  of  goods  was  1 450  and  the  dis- 
counts allowed  were  25%,  33 J%,  and  10  %.  Find  the  total 
discount  allowed. 

4.  I  allowed  a  customer  discounts  of  50%,  10  %,  and  10  % 
from  a  list  price.  What  per  cent  better  would  a  single  dis- 
count of  65  %  have  been  ? 

5.  Goods  were  sold  subject  to  trade  discounts  of  25  %,  20  %, 
and  10  %.  If  the  total  discount  allowed  was  1 460,  what  was 
the  net  selling  price  of  the  goods  ? 

6.  A  quantity  of  goods  was  sold  subject  to  trade  discounts 
of  20  %  and  20  % .  The  terms  were  60  da.  net  or  5  %  off  for 
payment  within  10  da.  If  a  cash  payment  of  11026  was  re- 
quired 3  da.  after  the  date  of  the  bill,  what  was  the  list  price 
of  the  goods  sold  ? 

307.  Since  the  first  of  a  series  of  discounts  is  computed  on 
100  %  of  the  list  price,  and  the  second  on  100  %  minus  the  first 
discount,  it  follows  that  the  sum  of  any  two  separate  discounts 
exceeds  the  equivalent  single  discount  hy  the  product  of  the  two 
rates  per  cent. 

Thus,  in  a  discount  series  of  20  %  and  20  %  the  apparent  single  discount  is 
the  sum  of  the  two  separate  discounts  or  40%;  but  shice  the  second  discount 
is  not  computed  on  100%,  but  on  80%,  40%  exceeds  the  true  single  discount 
by  20  %  of  20  %,  or  4% ;  and  the  equivalent  single  discount  is  40  %  minus  4  %, 
or  36  %.    Hence, 

308.  To  find  the  single  discount  equivalent  to  a  series  of 
two  discounts : 

From  the  sum  of  the  separate  discounts  subtract  their  product^ 
and  the  remainder  will  he  the  equivalent  single  discount. 

When  two  separate  discounts  cannot  be  reduced  to  a  single  discount 
mentally,  proceed  as  in  §  306  ;  when  they  can,  proceed  as  in  §  308. 


COMMERCIAL   DISCOUNTS  251 


ORAL   EXERCISE 


State  a  single  rate  of  discount  equivalent  to  a  discount  series  of : 

1.  10%  and  10%.  17.  50%  and  5%.  33.  25%  and  8%. 

2.  20%  and  20%.  18.  10%  and  5%.  34.  8^%  and  24%. 

3.  30%  and  30%.  19.  20%  and  5%.  35.  8|%and36%. 

4.  40%  and  40%.  20.  40%  and  5%.  36.  35%  and  10%. 

5.  50%  and  50%.  21.  25%  and  30%.  37.  20%andl2|%. 

6.  20%  and  10%.  22.  25%  and  40%.  38.  40%andl2i%. 

7.  30%  and  10%.  23.  20%  and  15%.  39.  60%andl2i%. 

8.  40%  and  10%.  24.  40%  and  15%.  40.  12%  and  121%. 

9.  50%  and  10%.  25.  35%  and  20%.  41.  24%andl6|%. 

10.  60%  and  10%.  26.  45%  and  20%.  42.  16|%and20%. 

11.  30%  and  20%.  27.  55%  and  20%.  43.  14|%and35%. 

12.  40%  and  20%.  28.  60%  and  25%.  44.  16|%and25%. 

13.  50%  and  20%.  29.  40%  and  25%.  45.  331%  and  15%. 

14.  60%  and  20%.  30.  60%  and  15%.  46.  66|%andl5%. 

15.  25%  and  10%.  31.  25%  and  331%.  47.  111%  and  18%. 

16.  35%  and  40%.  32.  45%and33J%.  48.  36%  and  111%. 

309.  When  a  discount  series  consists  of  three  separate  rates, 
the  first  two  may  be  combined  as  in  §  318  and  then  the  result 
and  the  third  may  be  combined  in  the  same  manner. 

310.  Example.  Find  a  single  rate  of  discount  equivalent 
to  a  discount  series  of  25%,,  20%?,  and  20%. 

Solution.  — Combine  the  first  two  by  thinking  25%  +  20%-  5%  =  40%,  the 
single  discount  equivalent  to  the  series  25 %  and  20 %.  20 %  +  40  %  -8 %  =  52 %, 
or  the  single  rate  equivalent  to  the  discount  series  25%,  20%,  and  20%. 

ORAL  EXERCISE 

State  a  single  rate  of  discount  equivalent  to  a  discount  series  of: 

1.  20%,  25%,  and  20%.  7.  20  %,  10%,  and  10%. 

2.  20%,  15%,  and  10%.  8.  40%,  10%,  and  10%. 

3.  20%,  20%,  and  20%.  9.  50%,  10%,  and  10%. 

4.  10%,  10%,  and  10%.  10.  30%,  10%,  and  10%. 

5.  20%,  20%,  and  10%.  11.  20  %,  25%,  and  10  %. 

6.  25%,  331%,  and  10%.  12.  20%,  20  %,  and  25%. 


252  PRACTICAL   BUSINESS   AEITHMETIC 

311.  When  it  is  not  desirable  to  show  the  separate  discounts, 
the  net  selling  price  may  be  found  as  shown  in  the  following 
example. 

312.  Example.  A  mahogany  sideboard  listed  at  $175  is 
sold  subject  to  trade  discounts  of  20%  and  25%.  Find  the 
net  cost  to  the  purchaser. 

Solution.  By  inspection  determine  that  a  100  %  —  40  %  =  60  % 
discount  of  40%  is  equivalent  to  a  series  of  25%  aQcf  of  ^175  =  S105 
and  20%.    Represent   the   gross  cost  by  100%. 

Then  100%  —  40%  =  60%,  the  net  cost  to  the  purchaser;  that  is,  the  net  cost 
of  the  sideboard  is  60%  of  the  list  price.  60%  of  ^  175  =  $  105,  the  net  cost  to 
the  purchaser. 

ORAL  EXERCISE 

Bt/  inspection  find  the  net  cost  of  articles  listed  at: 

1.  8400,  less  20%  and  25%.     5.    $1000,  less  50%  and  50%. 

2.  1300,  less  20%  and  20%.     6.    $1000,  less  30%  and  10%. 

3.  f  600,  less  10%  and  10%.     7.    |200,  less  60%  and  25%. 

4.  1200,  less  30%  and  30%.     8.    $400,  less  20%  and  40%. 

WRITTEN  EXERCISE 

-^  1.  Find  the  net  selling  price  of  a  piano  listed  at  $450,  less 
20%  and  20%. 

2.  Find  the  net  selling  price  of  an  oak  sideboard  listed  at 
$125,  less  25%,  3-31%,  and  10%. 

3.  I  bought  125  cultivators  listed  at  $8.50,  each  subject  to 
trade  discounts  of  20%  and  25%.  If  I  paid  freight  $30.50 
and  drayage  $7.90,  how  much  did  the  cultivators  cost  me? 

4.  The  net  cost  of  an  article  was  increased  $  30  by  freight, 
making  the  actual  cost  of  it  $  630.  What  was  the  list  price  of 
the  article,  the  rates  of  discount  being  25  %  and  33^  %  ? 

\  5.  You  desire  to  buy  24,000  ft.  choice  cypress :  one  firm 
quotes  you  $60  per  thousand  feet,  less  trade  discounts  of  20  % 
and  5%  ;  another  firm  offers  you  the  same  lumber  at  $75  per 
thousand  feet,  less  331%  and  8%.  The  terms  offered  by  both 
firms  are  Yio,  Vso*  ^^^  accept  the  better  offer  and. pay  cash. 
How  much  does  the  lumber  cost  you? 


COMMERCIAL  DISCOUNTS 


253 


WRITTEN  REVIEW  EXERCISE 

1.  Find  the  cost  of  125  1^"  brass  ells  at  $1.25  each,  less  25% 
20  %  and  10  f. 

2.  An  agent  bought  10  pianos  listed  at  8450  each,  less  33i% 
and  10  %,  and  sold  them  for  |400  each,  less  10  %  and  5  %.  Did 
he  gain  or  lose  and  how  much? 

3.  Apr.  15,  E.  L.  Gano  bought  of  W.  L.  Cunningham  &  Co. 
5  phaetons  listed  at  1450  each,  less  25%  and  20%.  Terms: 
Ygo,  ^/eo-     How  much  ready  money  would  settle  the  bill? 

4.  Study  the  following  bill.  Copy  and  find  the  net  amount 
of  it,  using  the  discounts  indicated  in  the  bill,  and  the  follow- 
ing prices:  windmills,  $675;  pumps,  S610;  1-in.  iron  pipe, 
Vl\j\  4-in.  iron  pipe,  73^;  hose,  97)^;  elbows,  21|j^;  valves, 
$1.49. 


Boston,  Ma55., 


a 


y>r^^//^, 


Terms. 


//a.  Yj/}^    /6o 


Bought  of  E.  M.  McGregor  &  co. 


^?^U^  ^^"/o  v^^  y. 


^^^U/^^^7^    V^v^^ 


ZS2 


Aroo_. 


ziT^. 


/■'Tn^ 


mm 


^;2^  WVlT^^-'T^C;^-,^-^ /^^^ 


2jni 


l-^o 


^^.-^^ 


^~7 


jL^ 


j^da 


^^  z.o'/>  "^z^y: 


2^Z\ 


liUl 


^^f^fo 


zAj.-. 


all: 


Ij2^ 


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jm. 


0^^y^y^^^  //^r^^^^ 


JZ^'- 


-^1 


.^?^^^  ^^  yl  y/^  y^ 


j^Al 


TJl 


.JIL 


1^ 


ll/^ 


JJL 


254  PEACTICAL  BUSINESS   AKITHMETIC 

.  5.  How  much  cash  would  settle  the  model  bill  (page  253) 
Oct.  30  ?  Nov.  8  ?  How  much  cash  would  settle  the  bill  called 
for  in  problem  4,  if  it  is  paid  for  on  the  day  it  is  written?  If 
it  is  paid  Nov.  15  ?  Copy  the  model  bill  in  the  form  that  it 
would  be  written  if  cash  accompanied  the  order ;  that  is,  copy  it 
deducting  the  3  %  allowed  for  immediate  payment. 

6.    Copy  and  find  the  net  amount  of  the  following  bill : 

NLeith,  Scotland,  May  lo.    19 

Invoice  of  Wire  Cloth 
Shipped  by  the  J.   M.    ROBERTS  COMPANY 

In  the  Steamship  Winifredian    To  Edward  M.  Davidson  &  Co. 

Philadelphia,  Pa. 


6  PC.  each  34'  x  5'  6"  1122  sq.  ft.  1/3  70  2  5 

6   "     "   40'  X  6'  6"   ****        1/4  ***  *  * 

5   "     "   42 '  X  7 '  4 "   ****        1/5  ***  **  * 

3   »     "   48'  X  7"  2"   ****        1/5   **  **  * 

««*  **  * 

Less  10%            **  **  * 


7.  E.  M.  French  &  Co.,  Albany,  N.Y.,  bought  of  Austin 
Bailey  &  Co.,  Boston,  Mass.,  Apr.  12,  3  doz.  pr.  hinges,  8  in.,  at 
$4.20,  and  3  doz.  pr.  hinges,  4  in.,  at  $2.10,  less  60%,  10%, 
and  10%  ;  50  lb.  brads,  |  in.,  at  90^,  and  50  lb.  brads,  |  in., 
at  80^,  less  50%,  10%,  and  5%.  Terms:  Vio,  Vao-  ^^^^^ 
the  net  amount  of  the  bill  Apr.  15. 

^^8.  D.  M.  DeLong,  Portland,  Me.,  sold  S.  H.  Shapleigh 
&  Co.,  Concord,  N.H.,  on  account  30  da.,  2%  10  da.:  35  cul- 
tivators listed  at  $7.50  each,  less  20%  and  10  %  ;  15  doz.  table 
knives  listed  at  $9.75,  less  10%  ;  15  doz.  hair  curlers  at  90^, 
less  5%  ;  15  doz.  locks.  No.  534,  at  $3.75,  less  10%  and  5%  ; 
I  doz.  steel  squares.  No.  8,  at  $36,  less  25%  and  10%  ;  1  gro. 
knives  and  ^rks.  No.  760,  at  $12,  less  20%  and  10%  ;  |  doz. 
cheese  knives  at  $9.75,  less  16|%.  Find  the  net  amount  of 
the  bill  5  da.  after  date. 


COMMERCIAL  DISCOUNTS  255 

WRITTEN  REVIEW  TEST 
(Time,  approximately,  forty  minutes) 

1.  If  goods  are  bought  25%  below  the  list  price  and  sold  at 
the  list  price,  what  is  the  advance  per  cent  over  the  cost  ? 

2.  If  goods  are  bought  20%  below  the  list  price  and  sold  at 
the  list  price,  what  is  the  advance  per  cent  over  the  cost  ? 

3.  If  goods  are  bought  10  %  below  the  list  price  and  sold  at  10  % 
above  the  list  price,  what  is  the  advance  per  cent  over  the  cost  ? 

4.  If  goods  are  bought  at  20%  and  12|%  below  the  list 
price,  and  sold  at  10%  below  the  list  price,  what  is  the  advance 
per  cent  over  the  cost  ? 

5.  A  hardware  dealer  bought  a  machine  listed  at  S24,  less 
16|%  and  10%,  and  sold  it  at  the  list  price.  At  what  per  cent 
above  cost  did  he  mark  the  selling  price  ? 

6.  A  jobber  wished  to  buy  at  such  a  discount  from  the  manu- 
facturer's list  price  that  he  could  make  an  advance  of  25%  over 
cost,  and  stiU  sell  at  the  manufacturer's  list  price.  What  would 
the  jobber  pay  for  SIOOO  worth  of  goods  ? 

7.  A  gentleman  wished  to  buy  a  carriage.  One  dealer  offered 
him  a  discount  of  33^%  and  10%  from  the  list  price,  and  an- 
other dealer  offered  him  20%,'  10%,  and  10%  from  the  list  price. 
If  the  list  price  is  S450,  what  will  be  the  cost  of  the  carriage  if 
it  is  bought  at  the  better  discount  ? 

8.  Aug.  5,  you  buy  of  Gray,  Salisbury  &  Son,  New  York 
City,  4000  lb.  raisins  at  16/,  less  trade  discounts  of  25%,  20%, 
and  10%.  Terms:  Vio,  ^Vso-  You  pay  cash  for  freight  $3.20. 
If  you  pay  the  bill  Aug.  7,  what  will  the  raisins  cost  you  ? 

9.  You  desire  to  buy  200  lb.  nutmeg.  You  find  that  S.  S- 
Pierce  Co.,  of  your  city,  offer  this  article  at  75/  per  lb.,  less  a 
discount  of  25%,  and  that  Smith,  Perkins  &  Co.,  New  York 
City,  offer  it  at  70/  per  lb.,  less  discounts  of  15%  and  10%. 
The  freight  from  New  York  to  your  city  on  a  package  of  this 
kind  is  S1.50.  The  terms  offered  by  both  firms  are:  Vio»  ^/so- 
You  accept  the  better  offer  and  pay  cash.  How  much  does 
the  nutmeg  cost  you  ? 


CHAPTER   XIX 

GAIN  AND  LOSS 
ORAL  EXERCISE 

^1.  What  is  33^%  of  8660?  How  much  is  gained  on  goods 
bought  for  1900  and  sold  at  a  profit  of  331%  ? 

•L2.  What  per  cent  greater  is  175  than  $60?  what  per  cent 
less  is  160  than  f  75?  Goods  bought  for  $100  are  sold  for 
$150.     What  is  the  gain  per  cent? 

3.  What  per  cent  less  is  $80  than  $100?  what  per  cent 
more  is  $100  than  $80?  Goods  bought  for  $100  are  sold  for 
$90.     What  is  the  loss  per  cent  ? 

4.  If  $800  is  increased  by  25%  of  itself,  what  is  the  result? 
Goods  bought  for  $1400  are  sold  at  a  profit  of  25%.  What  is 
the  selling  price  ? 

,5.  If  $1500  is  decreased  by  331%  of  itself,  what  is  the 
result?  Goods  bought  for  $2700  are  sold  at  a  loss  of  331%. 
What  is  the  selling  price  ? 

6.  State  a  brief  method  for  finding  a  gain  of  6|%;  a  gain 
of  6|%;  a  gain  of  81%;  a  gain  of  10%;  a  gain  of  l-|-%;  a  gain 
of  1|%;  a  gain  of  21%;   a  gain  of  31%. 

7.  State  a  brief  method  for  finding  a  loss  of  11^%;  a  loss 
of  121% ;  a  loss  of  14f  % ;  a  loss  of  16f  % ;  a  loss  of  20%  ;  a  loss 
of  25%  ;  a  loss  of  9^^  %  ;  a  loss  of  37^%. 

8.  State  a  brief  method  for  finding  a  gain  of  33^%;  a  gain 
of  22|%;;  a  gain  of  50%  ;  a  gain  of  66f  %;   a  gain  of  75  %. 

313.  The  gains  and  losses  resulting  from  business  transac- 
tions are  frequently  estimated  at  some  rate  per  cent  of  the  cost, 
or  of  the  money  or  capital  invested. 

Since  no  new  principles  are  involved  in  this  subject,  illustrative  examples 
are  unnecessary. 

256 


GAIN  AND  LOSS 


257 


FINDING   THE   GAIN   OR   LOSS 


( 

ORAL  EXERCISE 

By  inspection  find  the  gain  or  loss  : 

Per  Cent 

Per  Cent 

Per  Cent 

Cost       of  Gain 

Cost     of  Loss 

Cost 

OF  Gain 

1. 

12900     50%             9. 

$1500     10% 

17. 

$7500 

20% 

2. 

$1600     75%           10. 

$1600     1|% 

18. 

$1400 

25% 

3. 

15600     28f%         11. 

$3000     1|% 

19. 

$2200 

h\% 

4. 

$2700     331%         12. 

$4800     2J% 

20. 

$8100 

lli% 

5. 

12400     37i%         13. 

$3600     31% 

21. 

$6400 

12|% 

6. 

11400     42f%         14. 

$3200     61% 

22. 

$2800 

Wf% 

7. 

$3200     621%         15. 

$4500     6f% 

23. 

$9600 

161% 

8. 

$2100     66|%         16. 

$8400     81% 

24. 

$3600 

22|% 

25-48.    Find  the  selling  price  in  eacli  ( 

3f  the  above  problems. 

WRITTEN  EXERCISE 

1.  An  importation  of  silks  invoiced  at  £40  10s.  was  sold  at 
a  profit  of  25  % .  Find  the  amount  (in  United  States  money) 
of  the  gain. 

2.  An  importation  of  German  toys  invoiced  at  43,750  marks 
was  sold  at  a  gain  of  33  J  % .  Find  the  amount  (in  United  States 
money)  of  the  gain. 

3.  An  article  that  cost  $1  was  marked  10%  above  cost.  In 
order  to  effect  a  sale,  it  was  afterward  sold  for  10%  below  the 
marked  price.     Find  the  gain  or  loss  on  250  of  the  articles. 

'  4.  A  man  bought  a  city  lot  for  $1150  and  built  a  house  on 
it  costing  $2650.  He  then  sold  the  house  and  lot  at  a  gain  of 
5%.  How  much  did  he  gain  and  what  was  his  selling  price? 
^  5.  A  man  bought  a  quantity  of  silk  for  $450,  a  quantity  of 
fancy  plaids  for  $  120,  and  a  quantity  of  velvet  for  $  90.  He 
sold  the  silk  at  a  gain  of  25%,  the  plaids  at  a  loss  of  5  %,  and 
the  velvet  at  a  gain  of  331%.  What  was  his  gain,  and  how 
much  did  he  realize  from  the  sale  of  the  three  kinds  of 
material  ? 


258  PRACTICAL  BUSINESS  ARITHMETIC 

EmDING   THE   PER   CENT   OF   GAIN   OK  LOSS 

ORAL  EXERCISE 
By  inspection  find  the  per  cent  of  gain  or  loss : 


Cost 

Gain 

Cost 

Loss 

^^„     Selling 
C^^:^     Price 

i- 

Selling 
Price 

Gain 

1. 

flOO 

$10 

7. 

$60 

$15' 

13. 

$80    $90 

19. 

$300 

$60^ 

2. 

$150 

$50 

8. 

$40 

$10 

14. 

$90    $80 

20. 

$115 

$23 

3. 

$140 

$70 

9. 

$90 

$45 

15. 

$60    $75 

21. 

$102 

$17 

4. 

1140 

$140 

10. 

$70 

$14 

16. 

$75    $60 

22. 

$420 

$60 

5. 

$200 

$400 

11. 

$80 

$16 

17. 

$10    $50 

23. 

$300 

$200 

6. 

$300 

$750 

12. 

$15 

$10 

18. 

$50  $10 

24. 

$700 

$100 

WRITTEN  EXERCISE 

1.  A  milliner  bought  hats  at  $15  a  dozen  and  retailed  them 
at  $3  each.     What  per  cent  was  gained  ? 

,  2.    A  stationer  bought  paper  at  $2  a  ream  and  retailed  the 
same  at  a  cent  a  sheet.     What  was  his  per  cent  of  gain  ? 

3.  A  dry-goods  merchant  bought  gloves  at  $7.50  a  dozen 
pair  and  retailed  them  at  $1.25  a  pair.  What  was  his  per  cent 
of  gain  ? 

4.  A  merchant  imported  50  gro.  of  table  knives  at  a  cost 
of  $1125.  Two  months  later  he  found  that  the  sales  of  table 
knives  aggregated  $920  and  that  the  value  of  the  stock  unsold 
was  $435.     Did  he  gain  or  lose,  and  what  per  cent  ? 

5.  An  importer  bought  a  quantity  of  silk  goods  for  £  400  5s. 
After  disposing  of  a  part  of  the  goods  for  $1200  he  took  an 
account  of  the  stock  remaining  unsold  and  found  that  at  cost 
prices  it  was  worth  $1047.82.  Did  he  gain  or  lose,  and  what 
per  cent  ? 

6.  Jan.  1,  F.  E.  Smith  &  Co.  had  merchandise  on  hand 
valued  at  $2500.  During  the  month  they  purchased  goods 
costing  $6000  and  sold  goods  amounting  to  $7500.  If  the 
stock  on  hand  at  cost  prices  Feb.  5  was  worth  $2500,  what 
was  the  per  cent  of  gain  on  the  sales  ? 


GAIN  AND  LOSS  259 

FINDING  THE   COST 


ORAL 

EXERCISE 

By  inspection 

find  the  cost: 

Loss      ] 

Rate  of  Loss 

Gain    Rate  of  Gain 

1.    1150 

10% 

7. 

$35 

20% 

2.    $100 

H% 

8. 

$79 

25% 

3.    8200 

H% 

.        9- 

$12 

iH% 

4.    1450 

mo 

10. 

$19 

16|% 

5.    $220 

6-1% 

11. 

$44 

22|% 

6.   1115 

81% 

12. 

$15 

331% 

Selling 

Rate 

Selling 

Rate 

Price 

OF  Gain 

Price 

OF  Loss 

13.    11050 

5% 

19. 

$950 

5% 

14.    $2040 

2% 

20. 

$900 

50% 

15.    $3600 

20% 

21. 

$150 

■6i  % 

16.    $1400 

16f% 

22. 

$550 

16f% 

17.    $1800 

12i% 

23. 

$240 

331% 

18.    $2400 

331% 

24. 

$490 

22|% 

25.  A  man  bought  a  machine  for  S  240.48.  For  how  much 
must  he  sell  it  to  gain  121%  ? 

26.  B  sold  a  farm  for  S2400,  thereby  losing  25%.  For  how 
much  should  he  have  sold  it  to  have  gained  10%  ? 

27.  By  selling  a  piano  at  $400  a  dealer  realizes  a  gain  of 
33i%.  What  would  be  the  selling  price  of  the  piano  if  sold 
at  a  gain  of  25  %  ? 

WRITTEN  EXERCISE 

1.  A  sleigh  was  sold  for  $64.80,  which  was  10  %  below  cost. 
What  was  the  cost  ? 

2.  An  office  safe  was  sold  at  $102,  which  was  20%  above 
cost.     What  was  the  cost  ? 

3.  A   merchant  marks  goods  16|%  above  cost.     What  is 
the  cost  of  an  article  that  he  has  marked  $21.70? 


260  PRACTICAL   BUSINESS   ARITHMETIC 

4.  An  owner  of  real  estate  sold  2  city  lots  for  §12,000  each. 
On  one  he  gained  25%  and  on  the  other  he  lost  25%.  What 
was  his  net  gain  or  loss  from  the  two  transactions  ? 

5.  A  merchant  sold  a  quantity  of  goods  to  a  customer  at  a 
gain  of  25%,  but  owing  to  the  failure  of  the  customer  he  re- 
ceived in  settlement  but  88^  on  the  dollar.  If  the  merchant 
gained  $645.15,  what  did  the  goods  cost  him  ? 

6.  A  manufacturer  sold  an  article  to  a  jobber  at  a  gain  of 
25%,  the  jobber  sold  it  to  a  wholesaler  at  a  gain  of  20%,  and 
the  wholesaler  sold  it  to  a  retailer  at  a  gain  of  33J%.  If  the 
retailer  paid  $28  for  the  article,  what  was  the  cost  to  manufac- 
ture it  ? 

7.  A  manufacturer  sold  an  article  to  a  wholesaler  at  a  gain 
of  20%,  the  wholesaler  sold  the  same  article  to  a  retailer  at  a 
gain  of  33J%,  and  the  retailer  to  the  consumer  at  a  gain  of 
25%.  If  .the  average  gain  was  §40,  what  was  the  cost  to 
manufacture  the  article  ? 

WRITTEN  REVIEW  EXERCISE 

1.  A  merchant  bought  goods  at  40  %  off  from  the  list  price 
and  sold  the  same  at  20  %  and  10  %  off  the  list  price.  What 
was  his  gain  per  cent  ? 

2.  I  bought  goods  at  50%  off  from  the  list  price  and  sold 
them  at  25  %  and  25  %  off  frongi  the  list  price.  Did  I  gain  or 
lose,  and  what  per  cent  ? 

3.  Apr.  15  you  bought  of  Baker,  Taylor  &  Co.,  Rochester, 
N.  Y.,'4000  bbl.  Roller  Process  flour  listed  at  14.50  a  barrel, 
and  2000  bbl.  of  Searchlight  pastry  flour  listed  at  $4.75  a 
barrel.  Each  list  price  was  subject  to  trade  discounts  of  20% 
and  10%.  You  paid  cash  $16,000  and  gave  your  note  at  30  da. 
for  the  balance.      What  was  the  amount  of  the  note  ? 

4.  May  18  you  sold  to  F.  H.  Clark  &  Co.,  New  York  City, 
2000  bbl.  of  the  Roller  Process  flour,  bought  in  problem  3,  at 
331%  above  cost.  Terms:  Vio,  Vao-  ^''  H.  Clark  &  Co. 
paid  cash.     Find  the  cash  payment. 


GAIN  AND  LOSS  261 

5.  May  30  you  sold  Smith,  Perkins  &  Co.,  Albany,  N.Y., 
the  balance  of  the  :^ur  bought  in  problem  3,  at  an  advance 
of  33  J  %  on  the  costT^.Terms :  Vioi  Vao-  The  flour  was  paid 
for  June  8.     Find  the  cash  payment. 

6.  What  is  the  net  gain  on  the  transactions  in  problems  3, 
4,  and  5  ?  the  net  gain  per  cent  ? 

7.  Pec.  15  you  bought  of  E.  B.  Johnson  &  Co.  400  bbl.  of 
apples  at  ^2.50  per  barrel.  Terms  :  Vio^  Vso-  You  paid  cash. 
Find  the  amount  of  your  payment. 

8.  May  15  you  sold  F.  E.  Redmond  the  apples  bought  in 
problem  7,  at  $4  a  barrel.  Terms:  Vio^  Vso-  At  the 
maturity  of  the  bill  Redmond  refused  payment  and  you 
placed  the  account  in  the  hands  of  a  lawyer  who  succeeded  in 
collecting  75  %  of  the  amount  due.  If  the  lawyer's  fee  for  col- 
lecting was  4  ^,  what  was  your  net  gain  or  loss  ? 

9.  A  tailor  made  25  doz.  overcoats  with  cloth  worth  $2  a 
yard.  4  yd.  were  required  for  each  coat  and  the  cost  of 
making  was  $48  per  dozen.  He  sold  the  overcoats  so  as  to 
gain  33J^%.  •  How  much  did  he  receive  for  each? 

10.  Apr.  12  J.  D.  Farley  &  Son,  Trenton,  N.  J.,  bought  of 
Cobb,  Bates  &  Co.,  Boston,  Mass.,  a  quantity  of  green  Java 
coffee  sufficient  to  yield  2400  lb.  when  roasted.  If  the  loss  of 
weight  in  roasting  averages  4%,  what  will  the  green  coffee  cost 
at  30^  a  pound,  less  a  trade  discount  of  10%?  Arrange  the 
problem  in  bill  form. 

11.  If  the  coffee  in  problem  10  is  retailed  SS^%  above  cost, 
and  there  is  a  loss  of  1%  from  bad  debts,  what  is  the  gain  on 
the  transactions  in  coffee  ?  the  gain  per  cent  ? 

12.  The  Metropolitan  Coal  Co.,  of  Boston,  Mass.,  decides 
to  bid  on  a  contract  for  supplying  2240  T.  of  coal  for  the  pub- 
lic schools  of  the  city.  It  can  buy  the  coal  at  $4.50  per  long 
ton  delivered  on  board  track,  Boston.  It  costs  on  an  average 
75^  per  short  ton  to  deliver  the  coal,  and  there  is  a  waste  of  ^  % 
from  handling.  Name  a  bid  covering  a  profit  of  20%.  Terms: 
cash. 


262  PRACTICAL   BUSINESS  ARITHMETIC 

riNDING   THE   PER   CENT   OF   GAIK   OR   LOSS 
ON    THE   SELLING   PRICE 

ORAL  EXERCISE 

1.  An  article  cost  $80  and  it  is  sold  for  SIOO.  What  is  the 
sum  gained  ?  The  gain  is  what  per  cent  of  the  cost  ?  of  the 
selling  price  ? 

2.  An  article  costs  $60  and  it  is  sold  for  $75.  What  is  the 
sum  gained  ?  The  gain  is  what  per  cent  of  the  cost  ?  of  the 
selling  price  ? 

3.  An  article  is  sold  for  $90.  If  the  gain  on  the  selling  price 
is  33i%,  what  was  the  cost,  and  what  is  the  gain  per  cent  on 
the  cost  price  ? 

314.    Find  by  inspection  the  gain  per  cent  on  the  selling  price : 


Cost 

Selling  Price 

Cost 

Selling  Price 

a,    $20 

$30 

/.     $120 

$150 

h.   $30 

$40 

g.    $125 

$150 

c.    $45 

$60 

h.    $140 

$160 

d.    $60 

$75 

^.    $150 

•    $175 

e.    $50 

$60 

j.    $160 

$180 

This  principle  may  be  applied  effectively  when  goods  have  been  marked 
by  a  merchant  at  a  certain  per  cent  on  the  advance  of  the  cost,  and  then 
marked  down  to  sell  at  cost. 

315.  If  an  article  that  costs  $1  is  marked  to  sell  at  $1.10,  what 
per  cent  of  reduction  will  restore  the  original  cost  price  ? 

Suggestion.  It  is  evident  that  a  reduction  of  10%  on  the  selling  price 
will  not  restore  the  original  marking  of  $1. 

316.  Find  by  inspection  the  per  cent  of  reduction  that  must 
be  made  to  reduce  the  marked  price  to  the  cost  price. 

Cost  Marked  Price  Cost  Marked  Price 

a.    $1.00  $1.25  d.    $1.50  $1.80 

h.   $1.25  $1.50  e.   $2.00  $2.50 

c.    $1.60  $2.00  /.    $3.00  $4.00 

317.  Business  men  are  continually  dealing  with  the  problem 
of  overhead  charges;  that  is,  the  cost  of  doing  business.    Overhead 


GAIN  AND   LOSS  263 

charges  include  such  expenses  as  employees'  salaries,  rent,  insur- 
ance, taxes,  light  and  heat,  postage,  advertising,  depreciation, 
telephone,  and  many  others.  To  the  invoice  charges  there  must 
be  added  a  certain  per  cent  to  cover  the  cost  of  doing  business. 
318.  The  following  principle  applies  to  subsequent  problems: 
Divide  the  invoice  cost  plus  the  freight  by  100  %  minus  the  over- 
head charges  plus  the  per  cent  of  profit  (100  %  —  charges  +  profits) ; 
the  result  will  be  the  selling  price.  (This  statement  is  based  on 
reckoning  the  overhead  expenses  and  the  gain  as  a  per  cent  of 
the  selling  price.) 

WRITTEN    EXERCISE 

1.  An  article  was  invoiced  at  $33.50;  freight  charges,  S1.50. 
If  the  overhead  charges  amounted  to  15  %  and  the  gain  to  10  %, 
what  was  the  selling  price  ? 

Solution.     15% +  10%  =  25%. 

100% -25%  =  75%. 

^33.50  4-  '^l.SO  =  $35,  the  cost. 

.$35  -^  .75  =  $46.67,  the  selling  price. 
Proof.  25%  of  $46.67  =  $11.67,  overhead  charges  and  gain. 

$46.67-  $11.67  =  $35,  the  cost. 

2.  A  merchant  sold  goods  amounting  to  S  22,500.  If  the  over- 
head charges  amounted  to  18  %  and  the  profits  to  8  %,  what  was 
the  invoice  price  of  the  goods  if  the  freight  amounted  to  S  350  ? 

3.  A  merchant  marked  a  lot  of  goods  33i  %  above  cost,  but  as 
he  was  unable  to  sell  them  at  the  marked  price,  he  decided  to  reduce 
the  marking  to  cost.     What  per  cent  reduction  must  be  made  ? 

4.  A  machine  was  invoiced  at  S  53.50;  freight  charges,  S3.50. 
If  the  overhead  charges  of  the  business  amounted  to  20%,  and 
the  gain  to  10  %,  what  must  be  the  selling  price  of  the  goods  ? 

5.  An  invoice  of  merchandise  amounted  to  $1204.50;  freight 
charges,  $  10.50.  If  the  overhead  charges  amounted  to  17|  %  and 
the  gain  to  7^  %,  what  must  be  the  selling  price  ? 

6.  A  merchant  marked  a  lot  of  goods  at  25  %  above  cost,  but 
as  the  goods  did  not  sell  at  the  marked  price,  he  reduced  it  25  %, 
and  announced  that  he  was  selling  at  cost.  What  per  cent  rep- 
resents the  amount  of  his  error?  If  the  goods  thus  marked 
cost  $1760.48,  what  did  the  merchant  lose  by  his  blunder? 


CHAPTER  XX 

MARKING  GOODS 

319.  Merchants  frequently  use  some  private  mark  to  denote 
the  cost  and  the  selling  price  of  goods.  The  word,  phrase,  or 
series  of  arbitrary  characters  employed  for  private  marks  is 
called  a  key. 

Many  houses  use  two  different  keys  in  marking  goods,  one  to  represent 
the  cost  and  the  other  the  selling  price.  In  this  way  the  cost  of  an  article 
may  not  be  known  to  the  salesmen,  and  the  selling  price  may  not  be  known 
to  any  except  those  in  some  way  connected  with  the  business.  In  large 
houses,  when  but  one  key  is  used,  only  the  selling  price  is  indicated  on  the 
article,  it  being  deemed  best  to  keep  the  actual  cost  of  the  article  a  secret 
with  the  buyers.  In  small  houses,  when  but  one  key  is  used,  both  the  cost 
and  the  selling  price  are  frequently  written  on  the  article. 

320.  If  letters  are  used  to  mark  goods,  any  word  or  phrase 
containing  ten  different  letters  may  be  selected  for  a  key.  If 
arbitrary  characters  are  used,  any  ten  different  characters  may 
be  selected  for  a  key. 

Some  methods  of  marking  are  so  complicated  that  it  is  necessary  to 
always  have  a  key  of  the  system  at  hand  for  reference.  Goods  are  so  marked 
in  order  that  important  facts,  such  as  the  cost  of  goods,  may  be  kept  strictly 
private. 

321.  When  a  figure  is  repeated  one  or  more  times,  one  or 
two  extra  letters  called  repeaters  are  used  to  make  the  key 
word  more  secure  as  a  private  mark. 

322.  The  following  illustrates  the  method  of  marking  goods 
by  letters : 

Cost  Key  Selling-price  Key 

REPUBLICAN  PERTHAMBOY 

1234567890  1234567890 

Repeaters:  S  and  Z  Repeaters:  W  and  D 

264 


MARKING   GOODS 


265 


*^T    '^ 

n.u-u 

L  A.p  rt- 

-i 

The  cost  is  generally  written  above  and  the  selling  price  below  a  hori 
zontal  line  on  a  tag,  or  on  a  paster  or  box.  Gloves  No.  271, 
costing  $5  a  dozen  and  selling  for  $6.25  a  dozen,  might  be 
marked  as  shown  in  the  margin.  Fractions  may  be  desig- 
nated by  additional  letters  or  characters.  Thus,  W  may  be 
made  to  represent  |,  K  ^,  etc.  in  the  above  key.  In  marking 
goods  for  the  retail  trade,  all  fractions  of  a  cent  are  called  another  whole  cent. 

WRITTEN    EXERCISE 

323.    Using  the  keys  given  in  §  322,  write  the  cost  and  the  selling 
price  in  each  of  the  following  problems  : 


First  Cost 

OF 

Article  Freight    Gain 


1.  $2,50     10% 

2.  11.00     10% 

3.  .50 

f4.80 


20% 
20% 
331% 


4. 


20% 


Loss 


25% 


First  Cost 

OF 

Article      Freight 


2i% 


5.  $16.00 

6.  $40.00 

7.  I  3.60 

8.  |'24.00 


Gain 

1 

2 

'I 


37-i% 


161% 


2|% 


Loss 


10% 


324.    Using  the  following  hey,  write  the  cost  and  the  selling  price  in 
each  of  the  following  problems : 


Cost  Key 

Selling-price  Key 

r 

1 

L.1JhHCDJ-   + 

234567890 

T 

1 

xunE3fnuJi# 

234567890 

Repeaters :     □        C^s^ 

Repeaters :     X         — 

First  Cost 
of 
Article   Charges    Gain  Loss 

First  Cost 
of 
Article    Charges    Gain   Loss 

9. 
10. 
11. 

110.00       5%     20% 
120.00     10%     50% 
130.00     6|%            25% 

12. 
13. 
14. 

$15.00      6|%      25% 
$18.00      10%      25% 
$12.00       5%    331% 

325.  Wholesalers  and  jobbers  buy  and  sell  a  great  many 
articles  by  the  dozen.  Retailers  buy  a  great  many  articles  by 
the  dozen,  but  generally  sell  them  by  the  piece.  In  marking 
goods,  therefore,  it  is  highly  important  that  the  student  be  able 
to  divide  by  12  with  great  rapidity. 

To  divide  by  12  with  rapidity,  the  decimal  equivalents  of  the  12ths,  from 
rz  ^^\\  inclusive,  should  be  memorized. 


266 


PRACTICAL   BUSINESS  ARITHMETIC 


Table   of  Twelfths 


Twelfths 

Simplest 
Form 

Decimal 
Value 

Twelfths 

Simplest 
Form 

Decimal 
Value 

1^^ 

$.081 

A 

$.581 

A 

h 

.16f 

1% 

1 

.6()| 

A 

i 

.25 

A 

f 

.75 

T^^ 

i 

.33^ 

it 

1 

.83^ 

t\ 

An 

ii 

.91| 

A 

h 

.50 

11 

1 

1.00 

326.  Example.  What  is  the  cost  of  one  shirt  when  a  dozen 
shirts  cost  119  ? 

Solution.  Divide  by  12  the  same  as  by  any  number  of  one  digit  and  men- 
tally reduce  the  twelfths  in  the  remainder  to  their  decimal  equivalent.  Thus, 
say  or  think  l/^*  $1'58^5  practically  $1.58. 


ORAL 

EXERCISE 

State  the  cost 

per  i 

xrticle  when  the  cost  per  dozen  articles  is : 

1. 

125.00. 

7. 

•ifT.OO. 

13.    123.20. 

19. 

$9.00. 

2. 

137.00. 

8. 

13.60. 

14.    119.20. 

20. 

$7.00. 

3. 

!|42.00. 

9. 

12.40. 

15.    $66.60. 

21. 

$5.00. 

4. 

164.00. 

10. 

$5.60. 

16.    138.00. 

22. 

$7.50. 

5. 

180.00. 

11. 

13.40. 

17.    IIT.OO. 

23. 

$8.40. 

6. 

$13.00. 

12. 

113.20. 

ORAL 

18.    111.00. 

EXERCISE 

24. 

$17.50 

1.  Hats  costing  $48  a  dozen  must  be  sold  for  what  price 
each  to  gain  25  %  ? 

2.  Rulers  bought  at  $2  a  dozen  must  be  retailed  at  how 
much  each  to  gain  50  %  ? 

3.  Note  books  costing  $1.60   per  dozen  must   be   retailed 
at  what  price  each  to  gain  12|%  ? 

4.  Erasers  bought  at  $3.24  per  gross  must  be  retailed  at 
how  much  each  to  gain  1H\%  ? 

5.  Matches  costing  $3.60  per  gross  boxes  must  be  retailed 
at  what  price  per  box  to  gain  100%  ? 


MARKING   GOODS  267 

6.  Envelopes  bought  at  1 2  per  M  must  be  sold  at  what 
price  per  package  of  25  to  gain  100%? 

7.  Pickles  bought  at  il.80  per  dozen  bottles  must  be  sold 
at  what  price  per  bottle  to  gain  33  J  %  ? 

8.  Mustard  costing  $14.40  per  gross  packages  must  be  re- 
tailed at  what  price  per  package  to  gain  20%  ?  to  gain  50%  ? 

LISTING   GOODS   FOR   CATALOGUES 

327.  In  listing  goods  for  catalogues  dealers  generally  mark 
them  so  that  they  may  allow  a  discount  on  the  goods  and  still 
realize  a  profit. 

328.  Example.  What  should  be  the  catalogue  price  of  an 
article  costing  $24  in  order  to  insure  a  gain  of  25  %  and  allow 
the  purchaser  a  discount  of  20  %  ? 

Solution.     ^  of  ^24  =  .$6,  the  gain. 

^30  =  the  selling  price,  which  is  20%  below  the  catalogue  price. 

.80  of  the  catalogue  price  =  $30, 

.-.  the  catalogue  price  =  $30  -=-  .80  =  $37.50. 

WRITTEN  EXERCISE 

1.  At  what  price  must  you  mark  an  article  costing  $400  to 
gain  25  %  and  provide  for  a  20  %  loss  through  bad  debts  ? 

2.  What  should  be  the  catalogue  price  of  a  library  table 
costing  $25  in  order  to  insure  a  gain  of  20%  and  allow  the 
purchaser  a  discount  of  25  %  ? 

3.  You  list  tea  costing  30^  a  pound  in  such  a  way  that  you 
gain  33i  %  after  allowing  the  purchaser  a  trade  discount  of 
20  %.      What  is  your  list  price? 

4.  You  buy  broadcloth  at  $3.80  per  yard.  At  what  price 
must  you  mark  it  in  order  that  you  may  allow  your  cash 
customers  5  %  discount  and  still  realize  a  gain  of  20  %  ? 

5.  Having  bought  a  quantity  of  oranges  for  $3.00  per  C 
you  mark  them  so  as  to  gain  33^  %  and  allow  for  a  20  %  loss 
through  bad  debts.  What  will  be  your  asking  price  per 
dozen? 


268 


PEACTICAL   BUSINESS  ARITHMETIC 


6.    At  what  price  must  the  articles  in  the  following  invoice 
be  listed  to  gain  20  %  and  allow  discounts  of  25  %  and  20  %  ? 

Boston,  Mass.,        Nov.    24,   19 

Mr,   Edgar  C.  Townsend 

Rochester,  N.Y. 

Bought  of  WELLS,  FOWLER  &  CO. 

Terms  Net   50  da.  " 


400 
300 

630 

700 
70 

#721500ak  Bookcases  |8.00 

#924  25  Gentlemen's  Chiffoniers     12.00 

Less  10^ 

WRITTEN  REVIEW  EXERCISE 

1.  Using  the  word  importance^  with  repeaters  s  and  w^  for 
the  buying  key,  and  the  words  huy  for  cash,  with  repeaters  t 
and  m,^  for  the  selling  key,  write  the  cost  and  selling  price  of 
the  articles  in  the  following  bill.  It  is  desired  to  gain  25  %  on 
the  pens  and  pencils,  20  %  on  the  cards,  and  to  provide  for  a 
loss  of  12|  %  through  bad  debts. 

Boston,  Mass.,        Oct.   18,    19 

Messrs.  WHITE  &  WYCKOFP 

Holyoke,   Mass. 

Bought  of  C.  E.  Stevens  &  Co. 

Terms  Net  30  da. 


100 
25 
50 


gro.  Pens 

"  Lead  Pencils 
pkg.  Record  Cards 

Less  12  1/25^ 


$0.80 

80 

3.20 

80 

.40 

20 

180 

22 

50 

157 

50 


MARKING   GOODS 


269 


2.    At  what  price  must  I  mark  the  following  shoes  to  gain 
20%? 


M- 


^..  "7^^^?:; J. 


'Detroit^  Mich..,. 


^^.^^1^7^/r  7, 


/ ^  ' "    /^ 


■'9 


-^^./j^y^^a^ 


Terms. 


//a^     /ie 


Bought  of  ATWOOD  &  RANDALL 


3^^ 


^y^yU^J^^^^^^^-^:^^. 


^^^-^  ^V. 


^^:r/^^J^7„  /f 


^^ 


72=Z^ 


>^. 


-^^ 


-^A&A/MramA  (fCniA/^cA^tJiM 


^ 


3.  You  list  tea  bought  for  30^  at  an  advance  of  33^%  on 
the  cost.  Finding  small  sale  for  the  article  you  determine  to 
sell  so  as  to  gain  but  16|  % .  What  trade  discount  should  you 
allow  ? 

4.  What  price  per  pound  must  be  obtained  for  the  follow- 
ing invoice  of  coifee  to  gain  25  %  and  allow  10  %  for  loss  in 
roasting  and  16|  %  for  loss  through  bad  debts  ? 

^Boston,  ^Jtass.,  NoV.     25,     /9 

.-//Messrs.   Merchant   &   Co. 

120  Main  St.,    City 

thought  of  (^066,    fJjates   cP*    Go. 
!Terms    50    da. 


2000  lb.  Green  Java  Coffee  24^ 
Cartage 


480 
2 


00 
50 


482 


50 


CHAPTER   XXI 

COMMISSION  AND  BROKERAGE 
ORAL  EXERCISE 

1.  A  collected  a  bill  of  $350  and  received  6%  for  his 
services.     How  much  did  he  make  ? 

2.  B  bought  $80  worth  of  eggs  for  a  dealer  who  paid  him 
7J%  for  his  services.      How  much  did  B  make? 

3.  C  receives  $12  a  week,  and  5  %  of  his  weekly  sales.  If 
he  sold  $350  worth  of  goods  in  a  week,  what  was  his  income 
for  the  week  ? 

329.  An  agent  is  a  person  who  undertakes  to  transact  busi- 
ness for  another  called  the  principal. 

330.  A  great  deal  of  the  produce  of  the  country  and  a  large 
variety  of  manufactured  articles  are  bought  and  sold  through 
agents  called  commission  merchants  and  brokers. 

331.  A  commission  merchant  (sometimes  called  a  factor)  is 
an  agent  who  has  actual  possession  and  control  of  the  goods  of 
his  principal ;  a  broker  is  an  agent  who  arranges  for  purchases 
or  sales  of  goods  without  having  actual  possession  of  them. 

332.  The  sum  charged  by  an  agent  for  transacting  business 
for  his  principal  is  called  commission  or  brokerage. 

Commission  and  brokerage  are  frequently  computed  at  a  certain  per  cent 
of  the  amount  of  property  bought  or  sold,  or  of  the  amount  of  business 
transacted.  Brokerage  is  also  often  a  fixed  rate  per  bushel,  barrel,  tierce, 
or  other  standard  measure. 

333.  Agents  frequently  charge  an  additional  commission, 
called  guaranty,  for  assuming  any  risk  or  guaranteeing  the 
quality  of  goods  bought  or  sold. 

The  person  who  ships  goods  is  sometimes  called  the  consignor;  the  person 
to  whom  the  goods  are  shipped,  the  consignee. 

270 


COMMISSIOK   AND   BROKERAGE 


271 


A  quantity  of  goods  sent  away  to  be  sold  on  commission  is  called  a  ship- 
ment ;  a  quantity  of  goods  received  to  be  sold  on  commission,  a  consignment. 

334.  All  account  sales  is  an  itemized  statement  rendered  by  a 
commission  merchant  to  his  principal.  It  shows  in  detail  the 
sales  of  the  goods,  the  charges  thereon,  and  the  net  proceeds 
remitted  or  credited. 

SBuffalo,   J^.y.,       Zmt^q   18.    79 


^a/e  of  ^^^erchanctise  for  >^ccount  of 

E.  H.  Barker  &  Co..  Poughkeepsie. 


.Y. 


«^y    Zrlogg,    %/aylon 

cF"    >^ogg 

' 

June 

5 

200  bbl.    Roller  Process  Flour 

$6.00 

1200 

00 

12 

300      "        Old  Grist  Mill  Flour 
CAarges 

6.10 

1830 

00 

June 

2 

Freight  and  Drayage 

40 

75 

12 

Commission  5% 

151 

50 

18 

Net  proceeds  remitted 

2837 

75 

3030 

00 

3030 

00 

335.  An  account  purchase  is  a  detailed  statement  rendered 
by  a  purchasing  agent  to  his  principal.  It  shows  in  detail  the 
quantity,  grade,  and  price  of  goods  purchased,  the  expenses 
incurred,  and  the  gross  (total)  cost  of  the  transaction. 


Chicag< 

Purchase  of  Merchandise  for  Account 


.19- 


-y^^^^^^^^T^^-^^T^. 


By  GRAY.  DUNKLE  &  CO. 


^^^^r9- 


T^r} 


-X^>.&^^^^^^.^/^.,y^^       ■/ 


C(P(?  — 


^^2^__« ^^.d^J^C^^^^f^/z^^^ 


AJr: 


Adji 


2-/?^ 


Charges 


nS^^^ 


■2^:tZ. 


-.-rg-i^^ 


JJL 


JJI 


"(o.-r>-^^^3''j<;^^^L^<i^.'r7-7^^  2-y^ 


272  PRACTICAL  BUSINESS  ARITHMETIC 

ORAL  EXERCISE 

1.  I  sold  100  A.  of  land  at  ^50  per  acre  on  a  eommission  of 
3%.     What  was  my  commission? 

2.  A  lawyer  collected  an  account  of  $1000  and  received  for 
his  services  $40.     What  was  his  rate  of  commission  ? 

3.  A  book  agent  received  25  %  on  all  books  sold.  In  one 
week,  after  paying  his  expenses,  $25,  he  netted  $75.  What 
was  the  gross  amount  of  the  week's  sales  ? 

4.  I  bought  through  a  broker  1000  bu.  of  wheat  quoted  at 
89|^  per  bushel.  If  the  broker  charged  J^  per  bushel  for  buy- 
ing the  wheat,  what  was  his  brokerage  ?  How  much  did  the 
wheat  cost  me  ? 

SELLING   ON   COMMISSION 

WRITTEN  EXERCISE 

1.    Copy  and  complete  the  following  letter  : 
JOHNSON  &  CO. 

Produce  Merchants 


Boston,  Mass.,  ^/]/<g^V   / C?  .  ig 


(STUDENTS  NAME) 


JP\  (STUDENT'S  ADDRESS) 


COMMISSION   AND   BROKERAGE 


273 


2.  May  15  you  sell  F.  E.  Spencer,  Brattleboro,  from  John- 
son &  Co.'s  consignment :  200  tubs,  10,000  lb.,  creamery  butter 
at  23)^,  and  100  crates,  3000  doz.,  eggs  at  20)^,  f.o.b.  cars  Brat- 
tleboro. You  pay  freight  116  and  drayage  12.50.  The  terms 
are  y^),  ^/^q.  F.  E.  Spencer  pays  cash.  Make  a  receipted  bill 
for  the  transaction. 

3.  May  23  you  sell  Comstock  &  Co.,  Montpelier,  from  John- 
son &  Co.'s  consignment :  100  crates,  3000  doz.,  eggs  at  20  ^,  and 
100  boxes,  6000  lb.,  cheese  at  12^,  f.o.b.  Montpelier.  You  pay 
freight  |25  and  drayage  14.50.  Terms  :  V^q,  V30.  Comstock 
&  Co.  pay  cash.     Make  a  receipted  bill  for  the  transaction. 

4.  Render  Johnson  &  Co.  an  account  sales  under  date  of 
May  24  for  the  goods  shipped  May  10.  The  net  proceeds 
are  remitted  by  New  York  draft.     Commission,  5%. 

5.  Find  for  Johnson  &k  Co.,  the  net  gain  on  the  shipment 
in  problem  1.  The  eggs  were  bought  at  12)^,  the  creamery 
butter  at  15^,  and  the  cheese  at  S^.  Johnson  &  Co.  prepaid 
freight  on  shipment  to  you,  ^38.50. 

6.  Pay  freight  $>20.50  on  the  merchandise  enumerated  in  the 
following  shipping  invoice.  This  sum  is  5  %  of  the  cost  of  the 
goods.     Find  the  gross  cost  of  the  goods. 


New  Torky. 


^ 


^^-^.       f^.  TQ 


Invoice  of  Merchandise  shipped  to- 


(STUDENTS  NAME) 


(STUDENT'S  ADDRESS) 


To  be  sold  for  account  of  C,  L,  BROWN  ^  CO. 


^JL 


^ 


v-rz^. 


^^^T^T^^f:^^^^ 


^i!^ 


'.^^. 


>^Z^. 


^ 


7.  Dec.  15  you  sell  Morgan  &  Co.,  Albany,  N.Y.,  60  bx. 
lemons  at  $4.  Terms:  Viq,  Vso-  Morgan  &  Co.  pay  cash. 
What  is  the  amount  of  the  cash  payment  ? 


274  PRACTICAL   BUSINESS   ARITHMETIC 

8.  Dec.  18  you  sell  Meachum  &  Co.,  Troy,  N.Y.,  50  bx. 
oranges  at  $4.50.  Terms:  Vio^  Vso-  Meachum  &  Co.  pay  for 
the  goods  Jan.  12.     What  is  the  amount  of  their  payment? 

9.  Render  C.  L.  Brown  &  Co.  an  account  sales  for  the  goods 
received  Dec.  8,  commission,  5^.  Assume  that  on  Dec.  5  you 
advanced  them  $50  on  the  consignment.  Find  C.  L.  Brown 
&  Co's  net  gain  or  loss  on  the  shipment  in  problem  6. 

10.  Prepare  an  account  sales,  under  the  current  date,  for  the 
following,  sold  by  you,  for  the  account  of  Lewis,  Grayson  &  Co., 
Rochester,  N.Y. :  60  bbl.  Pillsbury's  flour  at  $6.25;  75  bbl. 
XXXX  flour  at  $5.75 ;  45  bbl.  star  brand  flour  at  $5  ;  100  bbl. 
XXX  flour  at  $4.90  ;  50  bbl.  peerless  flour  at  $5.15.  Charges  : 
freight,  $38.95;  cartage,  $12.60;  cooperage,  $6.25;  commis- 
sion, 31  %  ;  guaranty,  l%. 

BUYING   OX  COMMISSIOX 

WRITTEN  EXERCISE 

1.  B,  a  broker,  bought  for  C,  a  speculator,  3000  bu.  wheat 
at  90 J  ^,  on  a  commission  of  ^f^  per  bushel.  What  was  the 
broker's  commission,  and  what  did  the  wheat  cost  C? 

2.  I  bought  through  a  broker  5000  bags  coffee,  each  con- 
taining 130  lb.,  at  121^.  If  the  broker  charged  $10  for  each 
250  bags,  how  much  did  he  earn  on  the  transaction,  and  what 
did  the  coffee  cost  me? 

3.  I  bought  through  a  broker  20,000  bu.  of  wheat  at  Sl^-^f^, 
and  three  weeks  later  sold  it  through  the  same  broker  at  92|^. 
If  the  broker  charged  me  ^^  per  bu.  for  buying  and  the  same 
for  selling,  what  was  my  gain  ? 

4.  A  firm  of  produce  dealers  bought  through  a  broker  1500 
bbl.  pork  at  $12.50,  and  immediately  sold  it  through  another 
broker  at  $12.12^.  If  each  broker  charged  a  commission  of 
2J^  per  barrel,  what  was  gained  by  the  produce  dealers? 

5.  You  buy  for  your  principal  1500  bbl.  flour  at  $4.50,  on  a 
commission  of  3%,  and  pay  drayage  $18.50.  What  is  the  cost 
of  the  purchase  to  your  principal? 


COMMISSION   AND   BROKERAGE 


275 


6.  By  your  principars  instructions  you  put  the  flour  (prob- 
lem 5)  in  storage  and  later  sold  it  at  15.25  a  barrel,  on  a  com- 
mission of  3%.  The  storage  charges  were  5^  per  barrel. 
What  amount  should  you  remit  to  your  principal  ? 

7.  A  broker  bought  cotton  for  a  manufacturer  as  follows : 
750  bales,  375,000  lb.  at  lO-i  0 ;  1500  bales,  750,000  lb.  at  ^Of  ^; 
and  1000  bales,  500,000  lb.  at  lOf^.  The  broker's  charges  were 
$7.50  for  each  100  bales.  How  much  did  he  earn  on  the  trans- 
action, and  what  did  the  cotton  cost  the  manufacturers  ? 

8.  Find  the  amount  to  be  charged  to  Roe  &  Co. : 

New  York,  N.Y.,  Mar.  15,  19 
Purchased  by  Arault  &  Co. 

For  the  account  and  risk  of  Roe  &  Co. 

Telephone,  690  Main  Poughkeepsie,  N.Y. 


hf.  ch.  Japan  Tea  1200  # 

hf.  ch.  Oolong  Tea  1000# 

Charges 
Drayage 

Commission,  2%,  $      ;  guaranty,  ^%,  $ 
Amount  charged  to  your  account 


30^ 
45^ 


50 


9.    Find  the  rate  of  commission  and  the  amount  due  Brown 
Bros.  Co.  in  the  following  account  purchase. 


Rochester,  N.Y.,  Apr.  20,  19 
Purchased  by  Brown  Bros.  Co. 

For  the  account  and  risk  of  W.  D.  Snow 

Telephone,  1291  Main  Springfield,  Mass. 


600  bbl.  Pillsbury's  Best  Flour 
100  bbl.  xxxx  Flour 
200  bbl.  Peerless  Flour 

Charges 
Cartage 
Commission  ?  % 

Amount  due  us 


6.00 

5.50 

5.25 

15 

00 

104 

00 

276  PRACTICAL   BUSINESS   ARITHMETIC 

A  WRITTEN  REVIEW   TEST 

(Time,  approximately,  forty  minutes) 

Qofy  problems  1—12  and  complete  the  work  in  each  one : 


Face  of 
THE  Debt 

Rate  of 
Commission 

Amount  received 
BY  THE  Agent 

Amount  received 
BY  THE  Principal 

1. 

S457.75 

2% 

? 

? 

2. 

? 

1% 

$2.59 

? 

3. 

? 

? 

$5.27 

$170.23 

4. 

S  325.45 

? 

? 

$318.94 

5. 

S182.40 

5% 

? 

? 

6. 

S  255.50 

? 

$10.22 

? 

7. 

$112.75 

? 

? 

$108.24 

8. 

$282.00 

? 

$4.23 

? 

9. 

? 

%% 

? 

$251.55 

10. 

? 

? 

$14.84 

$409.16 

11. 

$455.95 

2% 

? 

? 

12. 

? 

? 

$6.60 

$125.40 

13.  A  commission  merchant  sold  5000  bu.  grain  and  charged 
IJ/  per  bushel  for  selling.  If  the  grain  was  sold  at  49/  per 
bushel,  what  sum  did  he  remit  to  his  principal  ? 

14.  The  net  proceeds  of  a  consignment  were  $593.75.  The 
following  were  the  different  charges :  commission,  $  26  ;  freight, 
$8.55;  drayage,  $  3.40  ;  storage,  $9.20  ;  advertising,  $  3  ;  insur- 
ance, $6.10.     What  was  the  rate  of  commission  ? 

15.  A  firm  of  contractors  employed  an  agent  to  collect  their 
overdue  accounts.  As  a  special  inducement  for  closing  the 
accounts,  they  were  to  give  him  6  %  on  all  collections  made  the 
first  month,  and  3i  %  on  all  collections  made  the  second  month. 
The  first  month  he  returned  to  the  firm  $4013.80;  the  second 
month  he  returned  $2798.50.  The  returns  were  made  after 
taking  out  his  commission.     What  was  the  agent's  commission  ? 


CHAPTER  XXII 

PROPERTY  INSURANCE 
FIRE   INSURANCE 

ORAL   EXERCISE 

1.  One  hundred  persons  have  property  valued  at  $500,000. 
They  pay  into  a  common  fund  60/  per  S 100  of  this  sum.  What 
is  the  amount  of  the  fund  ? 

2.  These  one  hundred  persons  live  in  widely  separated  parts 
of  the  country.  Is  it  likely  that  many  of  them  will  suffer  losses 
by  fire  in  the  same  year  ? 

3.  Suppose  the  losses  to  this  property  by  fire  for  a  year  amount 
to  S2500.  What  portion  of  the  common  fund  will  remain  on 
hand  as  a  surplus  ?     (No  interest.) 

4.  If  this  surplus  is  divided  among  the  hundred  persons  at  the 
end  of  the  year,  how  much  should  A,  who  paid  in  S  30,  receive  ? 

5.  What  are  the  companies  organized  to  receive  and  distribute 
the  fund  in  problem  1  called  ? 

336.  Insurance  is  a  contract  whereby  for  a  stipulated  con- 
sideration one  party  agrees  to  indemnify  another  for  the  loss  or 
damage  on  a  specified  subject  by  specified  perils,  according  to 
certain  prescribed  terms  and  conditions. 

The  best-known  forms  of  property  insurance  are  jire  insurance  and 
marine  insurance. 

There  are  also  property-insurance  companies  which  insure  against  loss 
due  to  steam-boiler  explosions,  failure  of  crops,  death  of  live  stock,  burglary, 
injury  to  business  by  strikes  among  employees,  and  numerous  other  hazards. 

337.  Fire  insurance  is  insurance  against  loss  of  property  or 

damage  to  it  by  fire. 

A  contract  of  fire  insurance  frequently  covers  loss  by  lightning  or  tornado. 
It  also  covers  damage  resulting  from  or  consequent  on  a  fire,  such  as  the  loss 

277 


278  PEACTICAL   BUSINESS  ARITHMETIC 

resulting  from  water  applied  for  the  purpose  of  extinguishing  flames, 
also,  for  the  loss  when  such  destruction  has  been  ordered  by  the  proper 
authorities. 

338.  The  insurer,  also  called  the  underwriter,  is  the  one  who 
agrees  to  indemnify.  The  insured  is  the  one  to  whom  the 
promise  of  indemnity  is  made.  The  premium  is  the  considera- 
tion agreed  upon  to  be  paid  by  the  insured.  The  policy  is  the 
written  contract  between  the  insurer  and  the  insured. 

339.  Fire  insurance' is  usually  conducted  under  the  joint  stock 
or  the  mutual  plan. 

In  a  joint  stock  company  capital  is  subscribed,  paid  for,  and  owned  by- 
persons  called  stockholders,  who  share  in  the  gains  and  are  liable,  to  the 
extent  of  their  subscriptions,  for  all  the  losses, 

A  mutual  insurance  company  is  one  in  which  all  the  f)olicy  holders  share 
the  gains  and  bear  the  losses  in  proportion  to  the  amount  of  the  premiums 
they  pay  to  that  particular  company,  and  their  fire  funds  consist  of  the 
reserve  earnings  and  the  results  of  investments. 

340.  Policies  of  insurance  are  of  various  kinds.  The  ordinary 
policy  is  a  contract  of  indemnity,  that  is,  a  contract  in  which  the 
amount  paid  in  case  of  loss  does  not  exceed  a  certain  specified 
sum;  this  sum  is  determined  by  evidence  after  the  loss  occurs. 
A  valued  policy  is  one  that  states  in  advance  the  amount  to  be 
paid  in  case  of  loss. 

Further  subdivisions  of  policies  are  as  follows  :  specific,  one  that  covers 
a  particular  kind  of  property,  as  a  single  building ;  blanket,  one  that  covers 
several  items  of  property,  as  a  group  of  buildings  and  the  contents ;  fixed, 
one  that  covers  property  at  some  particular  defined  location ;  floating,  one 
that  covers  specified  property  while  in  transit  or  in  various  defined  locali- 
ties ;  open,  one  which,  while  it  affixes  the  extreme  limit  of  the  amount  and 
duration  of  the  risk,  is  yet  open  to  secure  endorsements  granting  insurance 
in  various  amounts  and  places  at  any  time  and  for  any  period  that  may  be 
agreed  uj)on  at  the  time  of  the  endorsement ;  this  policy  is  used  largely  to 
protect  such  stocks  as  grain  in  elevators  or  as  the  contents  of  warehouses, 
and  the  records  are  usually  kept  in  a  book  known  as  an  open  policy  hook. 

341.  The  standard  forms  of  contract  used  in  fire  insurance 
policies  are  prescribed  by  the  state. 

These  forms  not  only  define  the  maximum  amount  and  the  term  for 
which  the  company  is  liable  but  also  the  consideration  paid  by  the  insured, 


PROPERTY   INSURANCE  279 

the  conditions  under  which  the  contract  will  become  void,  the  methods 
to  be  followed  in  the  settlement  of  a  loss,  and  the  procedure  to  effect  the 
cancellation  of  the  contract. 

If  a  loss  either  total  or  partial  occurs  under  such  a  policy,  the  company- 
is  bound  to  pay  only  so  much  of  the  sum  stated  in  the  policy  as  will  in- 
demnify the  insured;  e.g.  if  a  building  insured  for  $3000  is  damaged  by 
fire  $400,  only  the  actual  loss,  $400,  can  be  recovered;  but  if  the  same 
building  were  damaged  by  fire  $3500,  the  company  could  not  be  held  for 
more  than  $3000,  the  sum  stated  in  the  policy. 

342.  Average  and  co-insurance  clauses.  Where  a  number  of 
detached  properties  are  msured  under  one  poHcy,  it  is  customary 
to  attach  what  is  known  as  an  average  clause  which  specifies  that 
the  amount  of  insurance  covering  any  one  particular  piece  of 
property  shall  bear  such  proportion  to  the  total  amount  of  insur- 
ance on  the  whole  as  the  value  of  that  special  piece  of  property 
bears  to  the  value  of  all  of  the  properties  so  covered. 

343.  Many  fire-insurance  policies  contain  what  is  known  as  a 
co-insurance,  or  a  reduced-rate,  clause.  Under  this  clause  the 
insured  party  agrees  to  keep  his  property  insured  for  a  certain 
percentage  of  its  value ;  failing  to  do  this,  the  company  or  com- 
panies insuring  him  are  liable  only  for  that  proportion  of  a  loss 
which  the  amount  they  insure  bears  to  the  specified  percentage 
of  the  sound  value  of  the  property  covered. 

Thus,  the  value  of  a  piece  of  property  is  $10,000,  and  the  insured  agrees 
to  keep  it  insured  for  80%  of  its  value,  or  $8000,  but  fails  to  do  so  and 
carries  only  $6000  insurance.  Should  a  loss  occur,  the  company  will  pay 
only  three  fourths  (f  ^^f )  of  the  amount  of  such  loss. 

344.  The  rate  in  fire  insurance  is  the  amount  to  be  paid  to 
secure  SlOO  of  indemnity  for  one  year. 

The  rate  is  based  on  the  character  of  the  risk;  the  greater  the  likeli- 
hood of  fire  the  higher  the  rate. 

When  policies  are  written  for  a  period  of  more  than  one  year,  a  reduc- 
tion is  usually  made  in  figuring  the  premium.  Illustrations  :  on  city  dwell- 
ings the  jiremium  for  five  years  is  charged  for  four  times  the  annual  rate ; 
if  written  for  three  years,  for  two  and  one-half  times  the  annual  rate. 

Rates  are  expressed  by  the  number  of  cents  charged  for  $  100  of  insurance. 
When  over  $1  per  hundred,  the  rate  is  often  stated  in  dollars  and  cents. 

Short  rates  are  those  used  for  a  term  of  less  than  one  year;  they  are 
proportionately  higher  than  the  annual  rates. 


280  PRACTICAL   BUSINESS   ARITHMETIC 

ORAL  EXERCISE 

1.  What  is  the  cost  of  $6500  insurance  at  80/  per  SlOO? 

2.  What  is  the  premium  on  a  $  4000  policy  at  S  1.50  per  S 100  ? 

3.  What  is  the  cost  of  $6000  insurance  at  75/  per  $100  ? 

4.  B  insures  a  $6000  barn  for  |  value  at  50/  per  $100. 
What  quarterly  premium  should  he  pay  ? 

5.  A  insures  a  $6000  house  for  |  value,  at  50/  per  $100. 
What  is  the  semiannual  premium  ? 

6.  Goods  worth  $3000  are  insured  for  |-  value.  If  the 
annual  premium  is  $  30,  what  is  the  rate  ? 

7.  I  insure  $  2400  worth  of  merchandise  for  |  of  its  value  at 
60/  per  $100.     What  premium  must  I  pay? 

8.  I  insure  a  stock  of  goods  worth  $8000  for  $6000  at  2%. 
The  goods  become  damaged  by  fire  to  the  extent  of  $3000. 
Under  an  ordinary  policy  how  much  can  I  recover  ?  What  will 
be  my  net  loss,  premium  included  ? 

9.  A  brick  schoolhouse  is  insured  at  50/  per  $100,  the 
annual  premium  is  $50,  and  the  face  of  the  policy  |  of  the 
value  of  the  building.     What  is  the  value  of  the  building  ? 


ORAL    EXERCISE 

State  the  premium  in  i 

meh  of  the  following  problems : 

Face 

Face 

OF  Policy 

Rate 

OF  Policy 

Rate 

1. 

$1600 

4% 

3.    $3500 

$1.10 

per 

$100 

2. 

$1000 

n% 

4.     $5000 

$1.20 

per 

$100 

State  the  face  of  the  policy  in  each  of  the  following  problems : 

Premium               Rate  Premium                        Rate 

5.  $9                  2%  7.    $13.50         $1.35  per  $100 

6.  $15              11%  8.    $24.00         $1.60  per  $100 

State  the  rate  of  insurance  in  each  of  the  following  problems : 

Face  Face 

of  Policy               Premium  of  Policy                Premium 

9.    $1700             $25.50  11.    $3200             $130.00 

10.    $1850             $37.00  12.    $6500               $40.00 


PROPERTY   INSURANCE 


281 


345.    The  following  is  an  extract  from  a  tariff,  or  rate,  book  for 
the  properties  shown  on  the  map  which  follows  this  schedule. 


MAIN   STREET,   SOUTH 


No. 

189 


193 

197 
199 


John  Smith  &  Co. 

Frame  carriage  factory 

Contents 
John  Smith 

Frame  dwelling 

Frame  stable  (private) 
William  Brown 

Frame  store  and  dwelling 

Contents  of  grocery  store 

Contents  of  dwelling 
203-205  James  Robinson 

Brick  mercantile  building 
Robinson  &  Co. 

Department  store 

Offices  second  and  third  floors 


SIDE 
Flat  Rate 

$1.75  c 
1.76  c 

$0.25  a 
1.00  a 

$0.40  c 
0.40  c 
0.40  a 

$0.70  a 

$0.70  c 
0.70  c 


STATE    STREET,   NORTH   SIDE 


244  James  Green 

Brick  store  and  dwelling 

National  Butter  Co. 

Dwelling 
248  Thomas  White 

Frame  stable 

White's  Livery 
252  Thomas  White 

Frame  dwelling  and  contents 
256  Town  of  Jonesville 

Brick  high  school 

Contents 
258  Samuel  Parker 

Brick  dwelling 
260  State  Street  Baptist  Society 

Brick  church  building 

Organ  and  other  contents 


$0.25  a 
0.25  c 
0.25  c 

$1.00  c 
1.00  c 

$0.25  a 

$0.50  a 
0.50  a 

$0.17  a 

$0.50  a 
0.50  a 


80%  Rate 

$1.23  c 
1.23  c 


$0.28  c 
0.28  c 
0.28  c 

$0.50  a 

$0.50  c 
0.50  c 


$0.17^  a 
0.17i  c 


$0.70  c 
0.70  c 

$0.17^  a 

$0.35  a 
0.35  a 

$0.12  a 

$0.35  a 
0.35  a 


The  letter  a  after  the  rate  indicates  that  the  insurance  on  this  property  can 
be  written  for  more  than  one  year  ;  that  is,  at  two  and  one-half  times  the  rate, 
for  a  three-year  policy,  and  at  four  times  the  rate,  for  a  five-year  policy. 

The  letter  c  after  the  rate  indicates  that  the  insurance  on  this  property  can 
be  written  for  one  year,  or  for  a  number  of  years,  at  yearly  rates. 

The  city  block,  page  282,  contains  properties  insured  under  the  above 
schedule  of  rates. 


282 


PRACTICAL  BUSINESS  ARITHMETIC 


J 


Diagram  of  a  City  Block 


INIain 
193  197 


Street 
199 


n 


244  248        262  256       258        2C0 

State  Street 


WRITTEN    EXERCISE 


r 


These  problems  apply  to  the  properties  shown  on  the  above 
diagram ;  also  to  the  tariff  of  rates  in  the  preceding  schednle. 
The  flat  rate  is  used  unless  the  co-insurance  clause  is  mentioned. 

1.  The  frame  carriage  factory  at  189  Main  Street  is  worth 
$7000.  The  contents  are  worth  S8000;  both  are  insured  at  | 
of  their  value.     What  is  the  amount  of  the  annual  premium  ? 

2.  The  frame  dwelling  at  193  Main  Street  is  worth  $  3400,  and 
the  contents,  S1200.  The  frame  stable  owned  by  the  same  party 
at  197  Main  Street  is  worth  $1500,  and  the  contents,  $1100. 
All  of  this  property  is  insured  for  1  yr.  at  a  |  valuation.  What 
is  the  annual  premium  ?    What  will  it  cost  to  insure  it  for  3  yr.  ? 

3.  The  store  and  dwelling  at  199  Main  Street  are  worth  $4800. 
The  contents  of  the  store  are  worth  $2400,  and  of  the  dwelling, 
$800.    What  will  it  cost  to  insure  the  property  for  1  yr.  ? 

4.  The  brick  mercantile  building  at  203-205  Main  Street  is 
worth  $20,000.  The  contents  of  the  first  floor  are  worth  $4500, 
and  of  the  second  and  third  floors,  $7500.  All  are  insured  at  a 
75%  valuation  for  1  yr.  What  is  the  amount  of  the  premium? 
A  fire  occurs,  and  the  building  and  the  contents  are  damaged  to  the 
extent  of  $4500.  If  the  policies  contained  an  80%  co-insurance 
clause,  how  much  will  the  insuring  company  have  to  pay  ? 


PEOPERTY   INSURANCE  283 

5.  Suppose  that  the  building  described  in  problem  4  was 
insured  in  Company  A  for  S  18,000  at  the  tariff  rate,  and  the  con- 
tents in  Company  B  for  S  10,000  at  a  rate  of  75/;  that  each 
company  had  an  80  %  co-insurance  clause  attached  to  its  policy ; 
that  the  building  was  damaged  to  the  extent  of  S  3000,  and  the 
contents,  $  2500.  How  much  would  each  company  have  to  pay  ? 
What  would  be  the  net  loss  to  the  owner  of  the  building  ?  to  the 
owner  of  the  contents?  (Premium  included  in  each  case,  but 
no  interest.) 

6.  The  brick  church  at  260  State  Street  is  worth  S  10,000, 
and  the  contents,  S3500.  The  property  is  insured  for  1  yr.  for 
$8100.  If  the  policy  contains  an  80  %  co-insurance  clause,  what 
is  the  net  loss  to  the  insurance  company  (premium  included)  if 
the  property  is  wholly  destroyed  by  fire  ? 

7.  If  the  brick  school  building  at  256  Main  Street  is  worth 
$15,000  and  the  contents  are  worth  $7500,  what  will  it  cost 
under  the  term  rule  to  insure  it  for  5  yr.  for  80  %  of  its  value  ? 

8.  For  insuring  the  frame  buildings  at  252  and  248  State 
Street,  and  the  contents  of  each  for  |  of  their  value,  the  owner 
pays  an  annual  premium  of  $22.50.  If  the  frame  stable  and  the 
contents  are  worth  ^  of  the  frame  dwelling  and  the  contents,  what 
is  the  value  of  each  building,  including  the  contents  ? 

9.  The  brick  store  and  the  dwellmg  at  244  State  Street  are 
worth  $15,000  ;  the  property  is  insured  in  three  companies  for  ^ 
of  its  value.  Company  A  carries  i  of  the  line  at  the  tariff  rate ; 
Company  B,  |  of  the  line  at  a  50  /  rate ;  Company  C,  the  re- 
mainder of  the  line  at  a  66|/  rate.  What  is  the  total  premium 
paid  ?  The  building  is  damaged  by  fire  to  the  amount  of  $6000. 
What  amount  will  each  company  pay  ? 

10.  I  insured  a  block  of  buildings  in  the  JEtna  Insurance 
Company  for  $75,000  at  an  annual  rate  of  75/.  The  jEtna 
afterwards  reinsured  $15,000  of  its  liability  under  my  policy  in 
t^e  Continental  Insurance  Company  at  75/,  and  $20,000  in  the 
German  American  Insurance  Company  at  the  same  rate.  The 
building  was  damaged  by  fire  $  20,000.  What  was  the  net  loss 
of  each  of  the  three  companies  ? 


284  PRACTICAL   BUSINESS   ARITHMETIC 

11.    All  of  the  Main  Street  buildings  shown  on  the  preceding 
diagram  were  purchased  by  one  party  for  the  following  sums : 


Frame  carriage  factory  No.  189 
Frame  dwelling  at  No.  193 
Frame  stable  at  No.  197 
Frame  store  and  dwelling  at  No.  199 
Brick  mercantile  building  at  203-205 


$7,000 

3,400 

1,500 

4,500 

20,000 

$36,400 


It  is  proposed  to  insure  them  under  a  blanket  form  of  policy 
at  a  60/  rate  for  |^  of  the  cost.  The  policies  have  an  average 
clause  attached.  Formerly  these  properties  were  insured  sepa- 
rately at  the  tariff  rates  for  I  of  the  above  values.  Will  the 
proposed  plan  of  insurance  cost  more  or  less,  and  how  much  for 
lyr.? 

Information  regarding  the  different  kinds  of  policies  is  given  on  page 
278 ;  the  student  is  referred  to  this  page  for  a  suggestion  regarding  the 
blanket  form  of  policy,  the  form  used  in  problem  12. 

12.  A  certain  man  owns  four  grain  warehouses,  and  carries 
an  insurance  of  $20,000  on  the  contents  of  them  all,  with  an 
average  clause  attached.  At  the  time  of  a  fire  which  damaged 
the  contents  of  warehouse  B  $1500,  and  the  contents  of  ware- 
house D  $  7000,  it  was  found  that  the  grain  in  each  warehouse 
was  of  the  following  values  :  warehouse  A,  $  3000  ;  warehouse  B, 
$6000;  warehouse  C,  $8000;  warehouse  D,  $10,000.  What 
must  the  insuring  company  pay  on  the  damaged  stock  in  ware- 
house B  ?  in  warehouse  D  ? 

MARINE   INSURANCE 

346.  Marine  insurance  is  insurance  against  loss  to  ships  and 
cargoes  by  perils  of  navigation. 

347.  In  marine  insurance,  the  policies  usually  contain  a  clause 
to  the  effect  that  if  a  vessel  or  cargo,  or  both,  are  valued  at  more 
than  the  amount  insured,  the  insurers  will  pay  only  such  part  of 
the  loss,  either  partial  or  total,  as  the  amount  insured  bears  to 
the  full  valuation.     This  clause  is  called  an  average  clause. 


PROPERTY   INSURANCE  285 

Thus,  should  a  vessel  valued  at  $20,000,  and  insured  for  $15,000,  become 
damaged  by  fire  to  the  extent  of  $8000,  under  an  average  clause  policy  the 
company  will  pay  three  fourths  (iooo§)  of  the  loss,  or  $6000.  Should  the 
same  vessel  and  cargo  be  wholly  destroyed,  the  company  will  pay  the  full 
$15,000,  which  is  three  fourths  of  the  entire  valuation.  In  order  to  be  fully 
protected  in  a  marine  risk,  the  insured  must  insure  his  property  for  full 
value.  Some  fire  insurance  policies  contain  a  clause  similar  to  the  average 
clause  of  marine  insurance  policies. 

WRITTEN  EXERCISE 

1.  A  vessel  valued  at  $50,000  is  insured  (average  clause 
policy)  for  $18,000  in  Company  A,  and  for  $17,000  in  Company 
B.  A  fire  occurs  by  which  the  vessel  is  damaged  $15,000. 
What  is  the  amount  to  be  paid  by  each  company  ? 

2.  I  paid  $25.40  for  insuring  a  shipment  of  goods  by  steamer 
from  Boston  to  Manila.  If  the  rate  was  1|  %,  less  20  %,  what 
was  the  face  of  the  policy  ?  If  the  face  of  the  policy  was 
equal  to  the  value  of  the  goods,  what  would  it  cost  to  make  the 
shipment  by  sailing  vessel  at  1|  %,  less  20%? 

3.  You  take  out  a  $7500  average  clause  policy  on  your  stock 
of  merchandise  worth  $9000.  The  premium  is  75^  per  $100, 
which  you  pay  in  advance.  A  fire  occurs  by  which  the  stock 
is  damaged  $3000.  Estimate  your  total  loss  and  the  net  loss 
to  the  company.      (Premium  included  in  each  case.) 

4.  A  of  Boston  instructed  B  of  Sidney,  Australia,  to  purchase 
$25,000  worth  of  hides.  B  made  the  investment  as  instructed 
and  charged  1J%  commission.  The  hides  were  then  shipped 
by  steamer  and  insured  at  1|  %  for  enough  to  cover  the  value  of 
the  hides  and  all  charges.  What  was  the  amount  of  the  policy 
and  what  was  the  premium  ? 

5.  A  of  New  York  ordered  B  of  Duluth  to  buy  on  commission 
6000  bu.  of  wheat  and  6000  bu.  of  corn.  B  bought  the  wheat 
at  92^  and  the  corn  at  57^  per  bushel,  and  charged  IJ^per 
bushel  commission.  Before  shipping  the  grain  to  A  by  boat, 
B  took  out  a  policy  of  insurance  at  1|  %  to  cover  the  cost  of  the 
goods  and  all  charges.  What  was  the  agent's  commission  ? 
the  insurance  premium  ?     What  did  the  grain  cost  A  ? 


CHAPTER   XXIII 

STATE  AND  LOCAL  TAXES 
ORAL  EXERCISE 

1.  How  are  the  expenses  of  towns,  cities,  counties,  and 
states  met  ? 

2.  A  has  property  worth  $5000  and  B  property  worth 
$10,000.     How  should  the  taxes  of  these  two  men  compare? 

3.  Mention  several  purposes  for  which  taxes  are  raised  in 
your  city  or  town. 

348.  A  tax  is  a  sum  levied  for  the  support  of  government, 
or  for  other  public  purposes.  Taxes  are  of  two  kinds :  direct 
taxes,  which  are  taxes  levied  on  a  person,  his  property,  or  his 
business  ;  indirect  taxes,  which  are  taxes  levied  on  imported 
goods,  and  on  tobacco,  liquors,  etc.,  produced  and  consumed  in 
the  United  States. 

The  expenses  of  town,  county,  city,  and  state  governments  are  met  by 
capitation  or  poll  taxes,  property  taxes,  and  license  fees.  The  expenses  of  the 
National  Government  are  met  chiefly  by  import  duties,  or  customs,  and  excise 
duties. 

349.  A  capitation,  or  poll  tax,  is  a  tax  sometimes  levied  on  each 
male  inhabitant  who  has  attained  his  majority.  A  property  tax  is 
a  tax  levied  on  real  estate  or  on  personal  property.  A  license  fee 
is  a  tax  paid  for  permission  to  engage  in  certain  kinds  of  business. 

Real  estate  and  personal  property  belonging  to  religious  or  charitable 
organizations  are  frequently  exempt  from  taxation. 

350.  Property  taxes  are  imposed  in  nearly  all  the  states  by 
practically  the  same  method,  namely  : 

1.  Officers  called  assessors  are  elected  in  every  city  and 
town,  whose  business  it  is  to  set  a  valuation  upon  all  property 
subject  to  taxation. 

286 


STATE  AND  LOCAL  TAXES         287 

2.  In  most  of  the  states  a  County  Board  of  Equalization 
reviews  the  original  assessments,  and  the  judgment  of  this 
body  is  subsequently  passed  upon  by  the  State  Board  of 
Equalization. 

3.  All  the  taxes  for  state  purposes  are  then  equitably  appor- 
tioned among  the  different  counties,  cities,  and  towns.  Each 
county,  city,  town,  and  school  district  also  levies  taxes  for  its 
own  local  expenses. 

351.  The  tax  rate  is  expressed  as  so  many  mills  on  the  dollar 
or  so  many  dollars  on  a  hundred  or  a  thousand  dollars. 

The  Federal  Income  Tax  law  was  approved  Oct.  13,  1913.  It  is  a  new 
provision  for  raising  revenue  to  support  the  National  Government.  Only 
a  few  leading  provisions  are  noted  here. 

Every  citizen  of  the  United  States,  whether  residing  at  home  or  abroad, 
and  every  person  residing  in  the  United  States,  though  not  a  citizen  thereof, 
who  has  an  annual  net  income  from  all  sources  in  excess  of  $  3000  will  be 
required  to  pay  a  normal  tax  of  1  %  on  such  entire  net  income  in  excess  of 
$3000  or  in  excess  of  ^4000  if  a  person  is  married  and  living  with  a  wife  or 
a  husband.  The  normal  tax  of  1%  is  also  imposed  on  corporations,  joint- 
stock  companies  or  associations,  and  insurance  companies. 

For  special  information  address  any  collector  of  internal  revenue. 

ORAL  EXERCISE 

1.  If  the  rate  of  taxation  is  12  mills  on  a  dollar,  how  much 
tax  must  I  pay  on  property  assessed  at  $  5000  ? 

2.  The  tax  rate  is  13  mills  on  a  dollar.  B  has  property 
valued  at  1 8000  and  assessed  at  |  value.     What  is  his  tax  ? 

3.  C  pays  1^%  tax  on  a  city  lot  100  ft.  by  150  ft.,  valued 
at  11  per  square  foot,  and  assessed  at  |  value.  What  is  the 
amount  of  his  tax  ? 

4.  What  tax  must  I  pay  on  $80,000,  at  5  mills  on  $1,  the 
collector's  commission  being  1  %  ? 

Solution.     .005  of  $80,000  =  $400,  the  property  tax. 

1  %  of  the  tax  = 4,  the  collector's  commission. 

$404,  my  total  tax. 

5.  What  tax  must  I  pay  on  $10,000  at  4^  mills  on  $1,  the 
collector's  commission  being  1  %  ? 


288  PKACTICAL   BUSINESS  AEITHMETIC 

6.  An  unmarried  man  has  a  net  annual  income  of  $4568.  If 
exemptions  are  allowed  amounting  to  $215,  what  income  tax 
will  he  have  to  pay  ? 

7.  A  married  man  living  with  his  wife  has  a  net  annual  income 
of  $5432.50.  If  exemptions  are  allowed  amounting  to  $384.25, 
what  income  tax  v/ill  he  pay  ? 

8.  A  collector  turns  over  to  the  county  treasurer  f  8000.  If 
his  commission  was  1^  %  what  amount  did  he  collect?  If  the 
property  taxed  was  worth  f  800,000,  what  was  the  rate  of  taxa- 
tion?    Express  this  rate  in  three  ways. 

9.  The  assessed  valuation  of  real  and  personal  property  in 
a  certain  city  is  1400,000,000.  The  city  has  a  bonded  indebt- 
edness of  i  2,000,000,  on  which  it  pays  4  %  interest.  Find  the 
tax  rate  necessary  to  pay  the  interest. 

WRITTEN  EXERCISE 

Find  the  total  tax: 

1.  Valuation,  $3600;  rate,  10.016;   3  polls  at  $2. 

2.  Valuation,  14550;  rate,  9^  mills;  1  poll  at  |1.50. 

3.  Valuation,  $2875;  rate,  10.0175;  1  poll  at  11.75. 

4.  Valuation,  $5600;  rate,  $1,121  per  $100;  1  poll  at  $2. 

5.  Valuation,  $6000;  rate,  $13.40  per  $1000;  2  polls  at 
$1.00. 

Find  the  valuation  : 

6.  Total  tax,  $3800;  rate,  $0,015;  100  polls  at  $2.00. 

7.  Total  tax,  $11,295;  rate  $1.40  per  $100;  250  polls  at 
$1.50. 

8.  Total  tax,  $8850;  rate,  $15.00  per  $1000;  225  polls  at 
$1.00. 

9.  In  a  town  1040  persons  were  subject  to  a  poll  tax;  the 
assessed  valuation  of  real  estate  was  $3,209,400,  and  of  personal 
property  $265,100.  The  polls  were  taxed  $1.25  each.  The  tax 
levy  was  $42,994.  What  was  the  tax  rate  ?  What  was  the  total 
tax  of  Charles  B.  Lester,  who  owned  real  estate  valued  at  $6450, 
and  personal  property  valued  at  $1250,  and  who  paid  for  2  polls? 


STATE  AND  LOCAL  TAXES         289 

10.  In  a  town  taxes  were  levied  as  follows :  state  tax,  $4287  ; 
county  tax,  19312.50 ;  town  tax,  193,156.20.  There  were  1850 
polls  assessed  at  ^2  each.  If  the  total  property  valuation  was 
$6,245,800,  what  was  the  tax  rate  per  thousand  ? 

11.  A  town  made  provision  by  taxation  for  the  following 
expenses:  public  schools  $18,180;  interest  on  borrowed 
money  $2106;  public  highways  $4720;  officials'  salaries  $4620; 
general  expenses  $11,746;  sinking  fund  $8000.  The  value  of 
real  and  personal  property  was  $  2,450,600,  and  2120  polls  were 
assessed  $1.50  each;  $4531.80  was  collected  from  license  fees. 
What  was  the  tax  rate  ? 

12.  A  died  leaving  property  valued  at  $47,950  to  B,  his  son, 
and  property  valued  at  $  17,500  to  C,  a  friend.  The  statutes  of 
the  state  in  which  these  three  live  provide  that  B,  a  lineal  heir, 
and  C,  a  collateral  heir,  shall  pay  to  the  state  an  inheritance  tax. 
The  rate  for  lineal  heirs  is  1%,  and  for  collateral  heirs  5%. 
What  inheritance  tax  must  B  and  C,  respectively,  pay  when 
they  come  into  possession  of  the  property? 

13.  A  city  made  the  following  appropriation  for  its  public 
schools:  teaching  and  supervision,  $36,000;  care  and  cleaning, 
$3360;  fuel,  $3000;  repairs,  $2000;  text-books,  $1700;  supplies, 
$1700;  printing,  $300;  contingent  fund,  $775;  truant  officer, 
$500;  evening  schools,  $1305;  transportation  of  pupils,  $600; 
kindergarten,  $1100;  manual  training,  $700.  The  assessed 
value  of  real  estate  was  $6,709,998  and  of  personal  property 
$2,130,002.     What  was  the  tax  rate  for  school  purposes  ? 

14.  An  agent  made  the  following  report  of  his  income  as  a 
basis  for  computing  his  income  tax : 

Salary  per  year $3500       Interest  on  money  loaned  .     .  $415 

Commissions 985       Dividends  on  bank  stock    .     .       50 

Dividends  on  preferred  stock  in  a  corporation $250 

If  the  dividends  received  were  exempt,  the  tax  having  been 
paid  by  the  corporations,  what  would  be  his  income  tax  if  he 
were  a  married  man  living  with  his  wife  ?  What  would  be 
the  mcome  tax  of  an  unmarried  man  havmg  the  same  income  ? 


290 


PRACTICAL   BUSINESS   ARITHMETIC 


352.  In  order  to  facilitate  clerical  work  a  table  may  be  used 
for  computing  taxes.  The  following  table  was  made  from  the 
published  tax  lists  of  a  city  in  Massachusetts: 


Tax  Table. 

Rate 

$18.60 

PER  $1000 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

0 

.0000 

.0186 

.0372 

.0558 

.0744 

.0930 

.1110 

.1302 

.1488 

.1674 

1 

.1860 

.2046 

.2232 

.2418 

.2604 

.2790 

.2976 

.3162 

.3348 

.3534 

2 

.3720 

.3906 

.4092 

.4278 

.4404 

.4650 

.4836 

.5022 

.5208 

.5394 

3 

.5580 

.5766 

.5952 

.6138 

.6324 

.6510 

.6696 

.6882 

.7068 

.7254 

4 

.7440 

.7626 

.7812 

.7998 

.8184 

.8370 

.8556 

.8742 

.8928 

.9114 

5 

.9300 

.9486 

.9672 

.9858 

1.0044 

1.0230 

1.0416 

1.0602 

1.0788 

1.0974 

6 

1.1160 

1.1346 

1.1532 

1.1718 

1.1904 

1.2090 

1.2276 

1.2462 

1.2648 

1.2834 

7 

1.3020 

1.3206 

1.3392 

1.3578 

1.3764 

1.3950 

1.4136 

1.4322 

1.4508 

1.4694 

8 

1.4880 

1.5066 

1.5252 

1.5438 

1..5624 

1.5810 

1..5996 

1.6182 

1.6368 

1.65.54 

9 

1.6740 

1.6926 

1.7112 

1.7298 

1.7484 

1.7670 

1.78.56 

1.8042 

1.8228 

1.8414 

In  the  table  the  rate  on  each  $1000  was  made  up  as  follows :  state  tax 
$.0807  ;  county  tax,  $.5643  ;  state  highways,  $.003 ;  city  tax,  $17,952.  The 
first  figure  of  the  number  of  dollars  assessed  is  given  at  the  left,  and  the 
second  one  at  the  top. 

353.    Example.    What  is  the  tax  on  a  valuation  of  $16,400? 

Solution.    Tax  on  $16,000  =  $297.00  (1000  times  .2976) 
Tax  on  400  =        7.44  (100  times  .0744) 

tax  on  $  16,400  =  $305.04 

WRITTEN  EXERCISE 

Using  the  tahle^  find  the  tax  on  the  following  valuations : 

1.  12485.  5.      18,478.         9.    $34,500.         13.    120,000. 

2.  $1200.  6.    113,200.        10.    $82,500.         14.    $27,800. 

3.  $1050.  7.    $14,700.        11.    $98,250.         15.    $71,690. 

4.  $4630.  8.    $18,400.        12.    $21,850.         16.    $89,800. 

Find  the  tax  on  the  following  valuations  when  the  collector's 
commission  is  1%  : 


17. 

$5500. 

21. 

$9500. 

25. 

$19,000. 

29. 

$21,000 

18. 

$7500. 

22. 

$8700. 

26. 

$26,000. 

30. 

$89,000 

19. 

$2900. 

23. 

$6500. 

27. 

$85,000. 

31. 

$-10,000. 

20. 

$4700. 

24. 

$7250. 

28. 

$78,000. 

32. 

$21,000 

CHAPTER   XXIV 

CUSTOMS  DUTIES 
ORAL  EXERCISE 

1.  The  expenses  of  tlie  National  Government  average  about 
$  2,250,000  per  clay.     What  is  this  per  year  ? 

Suggestion.     To  multiply  by  16,  multiply  by  10  and  add  |  of  the  result. 

2.  Name  five  sources  of  income  to  the  National  Government. 

3.  Name  ten  expense  items  of  the  National  Government. 

354.  Duties,  or  customs,  are  taxes  levied  by  the  National  Gov- 
ernment on  imported  goods.  They  are  imposed  in  two  forms : 
ad  valorem  and  specific.  An  ad  valorem  duty  is  a  certain  per 
cent  levied  on  the  net  cost  of  the  importation.  A  specific  duty 
is  a  fixed  sum  levied  on  each  article,  or  on  each  pound,  ton, 
yard,  or  other  standard  measure,  without  regard  to  the  cost. 

Ad  valorem  duties  are  not  computed  on  fractions  of  a  dollar.  If  the 
cents  of  the  net  cost  are  less  than  fifty,  they  are  rejected;  if  fifty  or  more 
than  fifty,  one  dollar  is  added  before  computing  the  duty. 

Some  articles  are  subjected  to  both  ad  valorem  and  specific  duties.  Be- 
fore specific  duties  are  estimated  allowance  is  usually  made^for  tare  and 
breakage.  Specific  duties  are  not  computed  on  fractions  of  a  unit.  Frac- 
tions less  than  ^  of  a  unit  are  rejected ;  fractions  ^  or  more  are  counted  a 
whole  unit.     The  long  ton  of  2240  lb.  is  used  in  computing  specific  duties. 

355.  A  tariff  is  a  schedule  exhibiting  the  different  rates  of 
duties  imposed  by  Congress  on  imported  articles.  A  free  list  is 
a  schedule  of  imported  articles  exempt  from  duty. 

356.  A  customhouse  is  an  office  established  by  the  National 
Government  for  the  collection  of  duties  and  the  entry  and 
clearance  of  vessels.  A  port  at  which  a  customhouse  is  estab- 
lished is  called  a  port  of  entry;  ports  of  entry  and  other  ports 
are  called  ports  of  delivery. 

291 


292  PEACTICAL   BUSINESS  ARITHMETIC 

The  United  States  is  divided  into  customs  districts,  each  with  a  head- 
quarters port.  Goods  arriving  must  be  entered  at  the  original  port  of  entry ; 
if  consigned  to  an  interior  port,  this  entry  is  a  transportation  entry,  but  at 
the  other  port  it  may  be  entered  either  for  consumption  or  the  warehouse. 

357.  In  the  most  important  ports  of  the  United  States  the 
customhouse  business  is  distributed  among  three  departments : 

1.  The  collector's  office,  which  takes  charge  of  the  entries  and 
papers,  issues  the  permits,  and  collects  the  duties. 

2.  The  surveyor's  office,  which  takes  charge  of  the  vessel 
and  cargo,  receives  the  permits,  ascertains  the  quantities,  and 
delivers  the  merchandise  to  the  importer. 

3.  The  appraiser's  office,  which  examines  imported  merchan- 
dise and  determines  the  dutiable  value  and  the  rate  of  duty  on 
same. 

One  package  of  every  invoice  and  one  package,  at  least,  out  of  every  ten 
similar  packages  is  sent  to  the  appraiser's  store  for  examination.  Merchan- 
dise in  bulk  and  all  heavy  and  bulky  packages  uniform  in  size  and  quantity 
of  contents  are  generally  examined  on  the  wharf. 

358.  A  manifest  is  a  memorandum,  signed  by  the  master  of  the 
vessel,  showing  the  name  of  the  vessel,  its  cargo,  and  the  names 
and  addresses  of  the  consignors  and  consignees.  An  invoice  is  a 
detailed  statement  showing  the  particulars  of  the  goods  imported. 

All  invoices  should  be  made  out  in  the  weights  and  measures  of  the  coun- 
try in  which  the  goods  are  purchased ;  and  if  the  goods  are  subject  to  an 
ad  valorem  duty,  they  must  be  invoiced  in  the  currency  of  the  country  into 
which  they  are  imported.  Invoices  over  $100  must  be  certified  before  a 
United  States  consul,  who  causes  three  copies  of  the  invoice  to  be  made. 
One  is  sent  to  the  collector  of  the  port  at  which  the  goods  are  to  be  entered, 
one  is  kept  on  file  in  the  consul's  office,  and  one  is  sent  to  the  importer. 

When  the  merchandise  is  loaded  on  board  the  vessel  the  shippers  are 
given  a  bill  of  lading  which  acknowledges  the  receipt  of  the  several  pack- 
ages and  agrees  to  deliver  the  same  at  destination.  The  vessel's  commander 
keeps  a  copy  of  the  bill  of  lading  and  from  the  several  that  have  been  issued 
makes  out  his  manifest  of  cargo.  The  shippers  mail  the  invoice  and  bill  of 
lading  to  the  purchaser,  who  fills  out  an  entry  therefrom  and  presents  it 
and  the  invoice  at  the  customhouse  where  the  duties  imposed  by  law  on  the 
several  classes  of  merchandise  are  collected  and  a  permit  issued  for  the  land- 
ing and  delivery  of  the  merchandise,  subject  to  examination. 


CUSTOMS   DUTIES 


293 


359.  The  values  of  foreign  coins  are  periodically  proclaimed 
by  the  Secretary  of  the  Treasury,  and  these  values  must  be 
taken  in  estimating  duties  unless  a  depreciation  of  the  value  of 
the  foreign  currency  expressed  in -an  invoice  shall  be  shown  by 
the  consular  certificate  thereto  attached.  The  following  esti- 
mate of  the  values  of  foreign  coins  was  recently  proclaimed. 


Values 

OF  Foreign  Coins 

Country 

Standard 

Monetary  Unit 

Value  in 
U.  8.  Gold 

Brazil 

Denmark,  Norway,  Sweden   . 
France,  Belgium,  Switzerland 

German  Empire 

Great  Britain 

Japan     

Mexico 

Netherlands 

Philippine  Islands    .... 
Russia 

Gold 
Gold 
Gold 
Gold 
Gold 
Gold 
Gold 
Gold 
Gold 
Gold 

Milreis 
Crown 
Franc 
Mark 

Pound  sterling- 
Yen 
Peso 
Florin 
Peso 
Ruble 

$    .546 

.268 
.193 
.238 
4.866i 
.498 
.498 
.402 
.500 
.515 

The  lira  of  Italy,  and  the  peseta  of  Spain,  are  of  the  same  value  as  the 
franc.  The  dollar,  of  the  same  value  as  our  own,  is  the  standard  of  the 
British  possessions  of  North  America,  except  Newfoundland. 

360.  Depositing  goods  in  a  government  or  bonded  ware- 
house is  called  warehousing. 

Many  importers  buy  foreign  goods  in  large  quantities,  withdraw  a  part  of 
them,  and  store  the  remainder  in  the  government  warehouse.  The  goods  so 
deposited  may  be  taken  out  at  any  time  in  quantities  not  less  than  an  entire 
package,  or  in  bulk,  if  not  less  than  one  ton,  by  the  payment  of  duties,  stor- 
age, and  labor  charges.  Foreign  goods  are  sometimes  bought  three  or  four 
months  earlier  than  they  can  be  placed  on  the  market  and  are  stored  in  the 
government  warehouse  until  they  are  seasonable.  In  this  way  importers 
are  able  to  make  better  selections  and  they  also  get  better  terms  and  prices. 

361.  A  bonded  warehouse  is  a  building  provided  for  the 
storage  of  goods  on  which  duties  have  not  been  paid. 

The  importer  must  give  bond  for  the  payment  of  duties  on  all  goods 
stored  in  a  bonded  warehouse.      Goods  left  in  the  government  warehouse 


294 


PRACTICAL   BUSINESS  ARITHMETIC 


beyond  3  yr.  unclaimed  are  forfeited  to  the  government  and  sold  under  the 
direction  of  the  Secretary  of  the  Treasury.  Goods  may  })e  withdrawn  from 
a  bonded  warehouse  for  export,  or  for  transfer  to  a  warehouse  in  another 
district,  without  the  payment  of  duty. 

362.  The  two  common  forms  of  entry  under  which  duties 
are  collected  are  known  as  consumption  entry  and  warehouse 
entry.  The  former  is  used  for  merchandise  entered  for 
consumption;  the  latter  for  merchandise  that  is  placed  in  a 
bonded  warehouse  under  charge  of  the  government  storekeeper. 

363.  Excise  duties  are  taxes  levied  on  certain  goods  produced 
and  consumed  in  the  United  States.  If  goods,  on  which  either 
excise  or  import  duties  have  been  paid,  are  exported,  the 
amount  so  paid  is  refunded.  The  amount  refunded  is  called  a 
drawback. 

Table  of  Duties  on  Certain  Imports 


Article  and  Description 


Axminster  rugs 

Barley,  48  lb.  to  the  bushel  .... 
Barley  malt,  34  lb.  to  the  bushel  .  . 
Beans,  60  lb.  to  the  bushel       .... 

Brussels  carpets 

Books , 

Butter 

Castile  soap 

Cheese 

China  and  porcelain,  undecorated    . 

Clocks     . 

Cotton  tablecloths 

Hay 

Ingrain  carpets 

Knit  woolens 

Manufactures  of  leather 

Manufactures  of  marble 

Plate  glass,  16"  x  24" 

Pocket  knives,  value  not  over  $1  per  doz. 
Potatoes,  60  lb.  to  the  bushel       ... 

Saccharin 

Silk  dress  goods 

Toilet  soap,  unperfumed 

Wheat 

Window  glass        


Duty 


Specific 


15^  per  bu. 
25^  per  bu. 
25^  per  bu. 


2i  f  per  lb. 

$2  per  T. 

Qtf  per  sq.  ft. 
(Shf  per  lb. 


\^f'  per  bu. 
If  per  lb. 


Ad 
Valorem 


50% 


25% 
15% 

10% 

20% 
50% 
60% 
35% 

20% 
35% 
30% 
45% 

35% 
10% 

50% 
10% 


CUSTOMS   DUTIES  295 

FINDING   A   SPECIFIC   DUTY 

ORAL  EXERCISE 

Using  the  table  on  page  294,  find  the  duty  on: 

1.  67,200  lb.  of  hay. 

2.  48,000  lb.  of  barley. 

3.  100  pc.  plate  glass  16"  x  24". 

4.  2400  lb.  of  window  glass  10^'  x  lb'\ 

5.  A  quantity  of  butter  weighing  1000  lb. 

6.  A  shipment  of  wheat  weighing  240,000  lb. 

7.  A  quantity  of  saccharin  weighing  2100  lb. ;  tare  100  lb. 

WRITTEN    EXERCISE 

1.  Using  the  table  on  page  204^  find  the  total  duty  on  : 
2500  bu.  potatoes ;  value,  S1200.  96,000  lb.  barley. 
1275  lb.  toilet  soap  ;  value,  $425.  24,000  lb.  beans. 
30,000  bu.  potatoes ;  value,  $15,000.       136,000  lb.  barley  malt. 

2.  What  is  the  duty  on  175  bx.  castile  soap,  each  weighing 
110  lb.,  if  5%  is  allowed  for  tare  ?      Invoiced  at  20/  per  pound. 

3.  Calculate  the  duty  on  10  hogsheads  of  saccharin  weighing 
1060-105,  1040-105,  1160-112,  1240-120,  1180-116,  1100-102, 
1090-101, 1100-100,  1005-100,  1210-118  lb.,  respectively. 

4.  Richard  Roe  &  Co.  imported  from  Canada  3750  bu.  of 
potatoes  invoiced  at  20^  per  bushel.  If  the  transportation 
and  other  charges  amounted  to  $187.50,  how  much  must  be  re- 
ceived per  bushel  for  the  potatoes  in  order  to  gain  25  %  ? 

FINDING   AN   AD   VALOREM   DUTY 

ORAL   EXERCISE 

Find  the  total  duty  : 

1.  On  40  clocks  invoiced  at  $4.50  each. 

2.  On  12  books  invoiced  at  $1.50  each. 

3.  On  25  doz.  pocket  knives  invoiced  at  50^  per  doz. 

4.  On  100  sq.  yd.  ingrain  carpet  invoiced  at  $1  per  yard. 


296  PRACTICAL   BUSINESS   ARITHMETIC 

WRITTEN   EXERCISE 

Find  the  duty  on  : 

1.  An  Axniinster  rug,  12'  x  18',  invoiced  at  <£10. 
For  the  values  of  foreign  coins,  see  page  293. 

2.  A  200  lb.  box  of  knit  woolen  goods  invoiced  at  £  100. 

3.  An  importation  of  cotton  table  cloths  invoiced  at  ^100. 

4.  An  importation  of  cotton  table  cloths  invoiced  at  £  255. 

5.  300  bx.  plate  glass,  each  containing  25  plates  16"  x  24". 

6.  20  Axminster  rugs,  each  12'  x  18',  invoiced  at  X8  6s. 
per  rug. 

7.  An  importation  of  Dresden  china,  undecorated,  invoiced  at 
100  fr. 

8.  An  invoice  of  knit  woolens  weighing  600  lb.  and  valued 
at  £315  12s. 

9.  200  blocks  of  marble,  each  10'  x  4'  x  2',  invoiced  at 
328,000  lira. 

10.  An  importation  of  leather  from  Sweden  invoiced  at 
6750  crowns. 

11.  400  yd.  of  Brussels  carpeting,  |  yd.  wide,  invoiced  at 
$2  per  yard. 

12.  4000  meters  of  Brussels  carpeting,  |  yd.  wide,  invoiced 
at  5  francs  per  meter. 

A  meter  equals  approximately  1.1  yd. 

13.  4800  meters  of  silk  dress  goods,  |  yd.  wide,  invoiced  at 
3.75  marks  per  meter. 

14.  A  case  of  silk  dress  goods  containing  200  yd.,  1  yd.  wide, 
invoiced  at  1000  marks. 

15.  An  invoice  of  leather  goods  from  the  Netherlands  in- 
voiced at  12,520  florins. 

16.  5  cs.  of  silk  dress  goods,  each  containing  200  yd.,  J  yd. 
wide,  invoiced  at  20  marks  per  yard. 

17.  I  bought  an  invoice  of  Swiss  clocks,  paying  10,750  fr. 
for  them  in  Geneva.  What  was  the  total  cost  of  the  clocks, 
including  the  duty  ? 


CUSTOMS  DUTIES 


297 


INVOICES   AND   ENTRIES 

WRITTEN  EXERCISE 

1.    At  what  price  per  pair  must  the  lace  curtains  in  the  fol- 
lowing invoice  be  sold  in  order  to  realize  a  gain  of  33J  %  ? 

No.  427  Manchester y  England,         Dec.   15,   zp 

Invoice  of  Lace 
Shipped  by  WILLIAM  P,  FIRTH  &  CO. 

In  the  Steamer  Catalonia  Ti?  R.    H.   White  Company 

Boston,    Uass. 


Marks 


317 


Quantity 


50  doz.  pr, 


Articles  and  Description 


Lace  Curtains 
Less  2% 


Insurance  and  Freight 
Packing  and  Carting 


60%  ad  valorem  duty 


3/2/6 


Extension 


*«*-**-«* 
#-»*-** 


4-10-6 
16-6 


2.    Find  the  total  cost  of  the  following  invoice: 

Antwerpy  Belgium,        Apr.  2.  /9 

iV/essrs.  A.  T.  Summers  &  Co. 

New  York  City 

Bought  of  SCHMIDT  &  WESTERFELDT 

Terms  30  da. 


PC    Black  Silk 

39.00.    40.50.    39.00, 
40.00.    41.00,    40.50 

Insurance  and  freight 

Cartage 

50%  ad  valorem  duty 


240  5   fr, 


Do  not  compute  duty  on  insurance  and  freight,  nor  on  cartage. 
39.00,  40.50,  etc,  above,  equal  the  number  of  meters  in  each  piece. 


298 


PKACTICAL   BUSINESS   AEITHMETIC 


3.    Copy  the  following  invoice,  supplying  the  missing  terms 

Bradford,  England,         Dec.   5,    19 

Invoice  of  Woolen  Goods 

Shipped  by    RADCLIFFE    &    SON 
In  the  Steamship  Winifredian  To  R.   H.   Stearns  &  Co. 


Terms  30  da. 


Boston,   Mass. 


R 
317 


25 


PC   Black  Wool  Crepon 
68   69   69   68   69   60   55   60 
56   54   60   60   60   68  68   60 
45   65   65   55   60  65   65   60  60 

Consul's  fee 


1544 


1/9 

*** 

* 

« 

14 

10 

*** 

* 

4.  If  the  foregoing  invoice  of  goods  were  entered  for  im- 
mediate consumption,  the  following  is  the  entry  that  would  be 
made  out.     Complete  the  computation  in  the  entry. 


Manifest 


No.  ^S'a       Invoiced  at  'A^H^WJ!?-'?^,  (o-n^r^^ 


19— 


INWARD  FOREIGN  ENTRY  OF  MERCHANDISE 


Impoiled  b; 


.-^^^^^^^ 


y^^^^^^ 


:i£^^^2s<Master      From 


^^2- 


Mark 


Packages  and  Contents 


Quantity 


Free  List 


35%  ad  valoreni 


Duty 


Total 


^X? 


/J  J-'/  -<5' 


5.  How  much  will  R.  H.  Stearns  &  Co.  have  to  receive  per 
yard  for  the  foregoing  goods  in  order  to  realize  a  gain  of  25%? 

6.  In  a  recent  year  the  receipts  from  customs  duties  were 
1318,000,000,  and  from  excise  duties,  $344,000,000.  The  cus- 
toms duties  for  this  year  were  what  per  cent  greater  than  the 
excise  duties  ?  The  excise  duties  were  what  per  cent  less  than 
the  customs  duties  ? 


CUSTOMS   DUTIES 


299 


7.    Find  the  dutiable  value  and  compute  the  duty  on  the  fol- 
lowing entries  of  merchandise : 


a. 


Manifest  No,  v^/<^ .  Invoiced  ?A^^^^XH^yf^^^.f-/%fh  /X^  \  9 

INWARD  FOREIGN  ENTRY  OF  MERCHANDISE 

Imported  byJ^'^^C^.,.^/^^:^!^,^^:?^^        In  the  Steamer"C^^?"7^^>^^-?^--/;^;<?g^ 
"-^ (n  (i^^nf-r;<^t:^,M^\tx    From  \:/rzZ-Z^^^      Amved^^^:2i^l9 


Packages  and  Contents 


Quantity 


Free 
List 


45%  ad 
valorem 


1.5%  ad  valorem 


Duty 


/r 
7^ 


^ys'- 


Zf^-^ 


'^ 


7<7^fL, 


There  is  no  duty  charged  on  the  value  of  the  steel  v^ire,  nor  on  the 
quantity  or  value  of  the  sewing  needles ;  but  the  values  of  both  of  these 
quantities  is  reduced  to  United  States  money  by  the  customhouse  officials 
for  statistical  purposes. 


h. 


Manifest  No.  7 /^ 


Invoiced  at ^^^^^-Tl^rTy^^.^^r^^^^y^^^.-^r^^y?^^ //,\ 9— 

ICHANDI 


INWARD  FOREIGN  ENTRY  OF  MERCHANDISE 

Ijpported  \iy'/pfU'.A^y^^'t^'^^^               the  Steamer  ^^-^^^'^^.'•^^^-(^^^ 
^<»^r^??p?'^^.<c<?^ aster    From  'Xyrz^yfH^-^-    ..    Arr\vtd-MzZ^22^:^i^ 


Quantity 


Free 
List 


55%  ad 
valorem 


25%  ad  valorem 


Duty 


^^L:^ 


A<r"^ 


/SJ£^- 


n 


1  kilogram  equals  about  2^  avoirdupois  pounds. 


INTEEEST   AND   BANKING 
CHAPTER   XXV 

INTEREST 
ORAL  EXERCISE 

1.  A  borrows  $100  of  B  for  1  yr.  At  the  end  of  the  year 
what  will  A  probably  pay  B  besides  the  face  of  the  loan  ? 

2.  C  puts  $  100  in  a  savings  bank  and  leaves  it  for  1  yr. 
What  can  he  draw  out  at  the  end  of  the  year  besides  the 
money  deposited  ? 

3.  If  you  wished  to  borrow  money  of  a  bank  in  your  town, 
what  rate  of  interest  would  you  have  to  pay  ? 

4.  If  you  loaned  a  man  1500  for  1  yr.,  what  would  you 
require  him  to  give  you  as  evidence  of  the  loan  and  security 
for  its  payment  ? 

364.  The  compensation  paid  for  the  use  of  money  is  called 
interest.  Interest  is  computed  at  a  certain  per  cent  of  the  sum 
borrowed.  This  per  cent  of  interest  is  called  the  rate,  and  the 
sum  upon  which  it  is  computed,  the  principal. 

The  rate  of  interest  allowed  by  law  is  called  the  legal  rate.  Persons  may 
agree  to  pay  less  than  this  rate,  but  not  more,  unless  a  higher  rate  by  special 
agreement  is  permitted  by  statute.  When  an  obligation  is  interest-bearing 
and  no  rate  is  mentioned,  the  legal  rate  will  be  understood.  An  agreement 
for  interest  greater  than  that  allowed  by  law  is  called  usury. 

365.  In  the  commercial  world,  12  mo.  of  30  da.  each,  or  360 
da.,  are  reckoned  as  1  yr. 

This  method  is  not  exact,  but  it  is  the  most  common  because  the  most 
convenient.  It  has  been  legalized  by  statute  in  some  states  and  is  gener- 
ally used  in  all  the  states. 

300 


INTEREST  301 

SIMPLE   INTEREST 
The   Day   Method 

oral  exercise 

1.  How  many  days  in  a  commercial  year  ? 

2.  What  part  of  a  year  is  60  da.  ?  6  da.  ?  What  is  the  interest 
on-$l  for  1  yr.  at  6  %  ?  for  60  da.  ?  for  6  da.  ? 

3.  How  do  you  find  .01  of  a  number?  .001  of  a  number? 
What  is  the  interest  on  $120  for  60  da.  at  6  %  ?  for  6  da.  ? 

4.  State  a  short  method  for  finding  the  interest  on  any  prin- 
cipal for  60  da.  at  6  %  ;   for  6  da. 

5.  1  da.  is  what  part  of  6  da.  ?  What  is.^  of  .001  ?  What  is 
the  interest  on  $1200  for  1  da.  at  6  %  ?  on  $180  ?  on  $1500  ? 

6.  State  a  short  method  for  finding  the  interest  on  any 
principal  for  1  da.  at  6  %. 

366.  In  the  foregoing  exercise  it  is  clear  that  0.001  of  any 
principal  is  equal  to  the  interest  for  6  da.  at  6%;  or  0.001  of  any 
'principal  is  equal  to  6  times  the  interest  for  1  da.  at  G^fc 

ORAL  EXERCISE 

1.  Find  the  interest  on  each  of  the  following  for  6  da.  at  6%. 
a.  $250.  e.  $560.  ^.  $678.  m.  $290.  q.  $890. 
h.    $870.          /.    $435.       j.    $320.        n.    $150.       r.    $750. 

c.  $358.         g.    $430.       k.    $100.        o.    $325.       s.    $580. 

d.  $350.         h.    $470.        I.    $185.       p.    $990.       t.    $625. 

2.  Find  the  interest  on  each  of  the  above  amounts  for  12 
da.  at  6  %  ;  for  18  da. ;  for  24  da. 

3.  Find  the  interest  on  each  of  the  following  for  1  da.  at  6%. 


a. 

$360. 

e.    $660. 

i.    $600. 

m.    $480. 

q.    $840. 

h. 

$450. 

/.    $900. 

j.    $180. 

n.    $780. 

r.    $200. 

c. 

$300. 

g.    $540. 

h.    $720. 

0.    $400. 

s.    $330. 

d. 

$420. 

h.    $240. 

I.    $500. 

p.    $120. 

t.    $960. 

4. 

Find 

the  interest 

on   each   of 

the   above    amounts   for 

3  da, 

,  2.iQ% 

,  ;   for  2  da. 

302  PRACTICAL   BUSINESS   ARITHMETIC 

367.   Example.     Find  the  interest  on  |450  for  54  da.  at  6  %. 

Solution.    Pointing  off  three  places  to  the  left  54  x  10.45  =  $24.30 

gives   $0.45,    or  6  times   the    interest   for   1    da.  |»24  30  —  6  =  S4  05 

Multiplying  this  result  by  54  gives   $24.30,    or  6  '     >    * 
times  the  interest  for  54  da.     Dividing  this  result  by  6  gives  $4.05,  the  required 

interest.  9 

By     arranging    the    numbers    as  shown    in    the  54  x  $0.45 

margin  and   canceling    the  work  is  greatly  short-  Tj,            =$4.05 

ened.  ^ 

WRITTEN  EXERCISE 

At  6^0  find  the    interest   on    each   of  the  following  problems. 
Reduce  the  time  expressed  in  months  and  days  to  days. 

Principal  Time 

13.  $375.80  2  mo.  15  da. 

14.  $300.00  3  mo.  19  da. 

15.  $171.15  1  mo.  14  da. 

16.  $120.00  4  mo.  14  da. 

17.  $211.16  6  mo.  16  da. 

18.  W^b.^^  1  mo.  10  da. 

ORAL  EXERCISE 

1.  What  is  the  interest  on  $800  for  6  da.  at  3  %  '^ 

Solution.     80^  is  the  interest  for  6  da.  at  6  %.     3%  is  |  of  0%;  therefore, 
^  of  80 j?,  or  40  (^,  is  the  interest  for  6  da.  at  3%. 

2.  If  the  interest  at  6%  is  $45,  what  is  the  interest  for  the 
same  time  at  3%  ?  at  12%?  at  2%  ?  at  1%  ?  at  1^%? 

3.  Formulate  a  short  method  for  changing  6%  interest  to 
8%  interest. 

Solution.     8%  is  \  more  than  6%;  hence,  the  interest  at  6%  increased  by 
I  of  itself  equals  the  interest  at  8%. 

4.  State  a  short  method  for  changing    6%  interest  to  7% 
interest;  to  5%  ;  to  9%  ;  to  7|%  ;  to  41%. 

5.  If  the  interest  at  6%  is  $120,  what  is  the  interest  at  7%? 
at  5%  ?  at  8%?     at  4%  ?  at  7^%?  at  ^%  ? 


Principal    Time 

Principal    Time 

1. 

$620  54  da. 

7. 

$900.00  29  da. 

2. 

$175  84  da. 

8. 

$865.45  93  da. 

3. 

$645  42  da. 

9. 

$700.00  96  da. 

4. 

$300  84  da. 

10. 

$974.30  62  da. 

5. 

$600  72  da. 

11. 

$178.45  40  da. 

6. 

$502  66  da. 

12. 

$438.55  50  da. 

INTEREST  303 

368.  In  the  foregoing  exercise  it  is  clear  that  6%  interest  in- 
creased hy  \  of  itself  equals  9  %  iyiterest;  hy  |  of  itself^  8  %  interest; 
by  ^  of  itself  7|  %  iyiterest;  hy  1  of  itself  7  fo  interest;  also  that 

6%  interest  decreased  hy  ^  of  itself  equals  4  %  interest;  hy  \of 
itself^  4\  <fo  interest;  hy  ^  of  itself  5%  inter  est  \  also  that 

6  %  interest  divided  hy  2  equals  3  %  interest ;  hy  3^  2ffo  inter- 
est; hy  6^  1%  interest;  hy  4,  i|  %  interest, 

6  %  interest  multiplied  by  2  equals  12  %  interest. 

6%  interest  is  changed  to  10%  interest  by  dividing  by  6  and  removing 
the  decimal  point  one  place  to  the  right ;  to  any  other  rate  by  dividing 
by  6  and  multiplying  by  the  given  rate. 

WRITTEN  EXERCISE 

Using  the  exact  number  of  days,  find  the  interest  on : 

1.  12500  from  Sept.  18,  1906,  to  Feb.  6,  1907,  at  9%  ;  at 
3i%;  at  4%;  at  3%. 

2.  11700  from  Nov.  20,  1906,  to  Jan.  16,  1907,  at  8%;  at 
21%;  at  51%;  at  31%;  at  4%. 

3.  12750  from  Dec.  16, 1906,  to  Jan.  17, 1907,  at  7%;  at  2%; 
at  4  %  ;  at  5  %  ;  at  1  %  ;  at  10 %. 

4.  16250  from  Dec.  18,  1906,  to  Feb.  6,  1907,  at  7^  %  ;  at 
10  %  ;  at  1|  %  ;  at  ^  %  ;  at  9  %  ;  at  8  % ;  at  7  %  ;  at  3  %. 

The  Banker's  Sixty-Day  Method 
oral  exercise 

1.  60  da.  (2  mo.)  is  what  part  of  a  commercial  year? 

2.  What  is  the  interest  on  $1  for  2  mo.  at  6%?  for  60  da.? 

3.  How  can  you  find  0.01  of  a  number?  What  is. the  interest 
on $50  for  60  da.  at  6%?  on  1 370?  on  $590?  on  1214.55? 

4.  What  fractional  part  of  60  da.  is  30  da.?  20  da.  ?  15  da.  ? 
10  da.  ?  What  is  the  interest  on  11680  for  60  da.  ?  for  30  da.  ? 
for  20  da.  ?  for  15  da.  ?  for  10  da.  ? 

5.  State  a  simple  way  to  find  the  interest  on  any  principal 
for  60  da.  at  6  %  ;  for  30  da.  ;  for  20  da. ;  for  15  da. ;  for 
10  da. 


304  PRACTICAL   BUSINESS   ARITHMETIC 

6.    Read  aloud  the  following,  supplying  the  missing  words: 
a.  60  da.  minus  ^^  of  itself  equals  bb  da. ;   60  da.  minus 


of  itself  equals  50  da.  ;  60  da.  minus of  itself  equals  40 

da.  ;  60  da.  minus of  itself  equals  45  da. 

5.    60  da.  plus  -^^  of  itself  equals  ^b  da. ;  60  da.  plus 

of  itself  equals  70  da. ;  60  da.  plus of  itself  equals  75  da. ; 

60  da.  plus of  itself  equals  80   da. ;  60  da.  plus of 

itself  equals  90  da. 

7.  What  is  the  interest  on  $600  for  60  da.  at  6%?  for 
bb  da.  ?  for  50  da.  ?  for  40  da.  ?  for  45  da.  ? 

8.  What  is  the  interest  on  $1200  for  60  da.?  for  ^b  da.? 
for  70  da.  ?  for  75  da.  ?  for  80  da.  ?  for  90  da.  ? 

9.  State  a  short  way  to  find  the  interest  at  6%  for  80  da. ; 
for  90  da. ;  for  50  da. ;  for  ^b  da. ;  for  55  da. ;  for  75  da. ;  for 
70  da.;  for  40  da.;  for  45  da. 

369.  In  the  above  exercise  it  is  clear  that  removing  the 
decimal  'point  two  places  to  the  left  in  the  principal  gives  the 
interest  for  60  da.  at  Q^c 

370.  Examples,  l.  Find  the  interest  on  $1950  for  20  da. 
at  6%. 

Solution.  Eemovlng  the  decimal  point  two  places  to  the  left  $19.50 
gives  the  interest  for  60  da.     20  da.  is  \  of  60  da.     \oi%  19.50  =  ojt^  cq 

^  D.  OU. 

2.    What  is  the  interest  on  $8400.68  for  75  days  ? 

Solution.  Removing  the  decimal  point  two  ^  g^  0068 
places  to  the  left  gives  the  interest  for  60  da.  ^^  ^^.j  „ 

75  da.  is 60  da.  increased  by  \  of  itself  ;  therefore  ^^-^^^ 


$84.0068  increased  by  \  of  itself  or  $105.01  is  $105.0085,  or  $105.01 
the  required  interest.  In  the  following  exercise  determine  the  separate  interest 
mentally  whenever  it  is  possible  to  do  so. 

WRITTEN  EXERCISE 

1.    Find'  the  total  amount  of  interest  at  6%  on: 
$8400  for  60  da.  $8400  for  12  da.  $7900  for  20  da. 

$8400  for  30  da.  $8400  for  10  da.  $7900  for  15  da. 

$8400  for  20  da.  $7900  for  60  da.  $7900  for  12  da. 

$8400  for  15  da.  $7900  for  30  da.  $7900  for  10  da. 


INTEREST  305 

2.  Find  the  total  amount  of  interest  at  6%  on:* 

$  1600  for  60  da.  1 1600  for  40  da.  1 2800  for  75  da. 

i  1600  for  55  da.  $  2800  for  60  da.  $  2800  for  80  da. 

$  1600  for  50  da.  1 2800  for  6b  da.  $  2800  for  90  da. 

$  1600  for  45  da.  $  2800  for  70  da.  $  7200  for  55  da. 

3.  Find  the  total  amount  of  interest  at  6  %  on  : 

$  1500.60  for  30  da.  $  832.60  for  90  da.  1 8575.65  for  70  da. 
i  1800.72  for  20  da.  $  720.18  for  10  da.  $  6282.40  for  15  da. 
i  1200.64  for  15  da.  $  440.70  for  40  da.  1 1460. 84  for  65  da. 
$  8400.60  for  10  da.     f  479.64  for  50  da.       $  1385. 62  for  55  da. 

4.  Find  the  total  amount  of  interest  at  6%  on  : 

$  1800.40  for  90  da.  $  7500.00  for  55  da.  $  216.90  for  20  da. 

$  9200.50  for  80  da.  $  8200.00  for  75  da.  $  432. 65  for  15  da. 

$  3240.64  for  70  da.  $  6400.00  for  45  da.  $  832.30  for  10  da. 

14125.18  for  45  da.  $  1200.45  for  30  da.  $  926.17  for  20  da. 

ORAL  EXERCISE 

1.  What  is  the  interest  on  §  215  for  6  da.  at  6  %  ?  on  $  345  ? 
on  1415?  on  8827.50?  on  1425.90?  on  $4520.60?  State  a 
simple  way  to  find  the  interest  on  any  principal  for  6  da. 
at  6%. 

2.  What  part  of  G  da.  is  3  da.  ?  is  2  da.  ?  is  1  da.  ?  What  is 
the  interest  on  $720  for  6  da.?  for  3  da.  ?  for  2  da.  ?  for  1  da.  ? 
State  a  brief  method  of  finding  the  interest  on  any  principal 
for  3  da.  at  6%;  for  2  da.;   for  1  da. 

3.  Read  aloud  the  following,  supplying  the  missing  words : 

a.  6  da.  minus  J  of  itself  equals  5  da. ;   6  da.  minus of 

itself  equals  4  da. 

b.  6  da.  plus  ^  of  itself  equals  7  da. ;  6  da.  plus of  itself 

equals  8  da. ;  6  da.  plus of  itself  equals  9  da. 

c.  State  a  short  method  of  finding  the  interest  at  6  %  for  4 
da. ;  for  5  da. ;  for  7  da. ;  for  8  da. ;  for  9  da. 

371.  In  the  above  exercise  it  is  clear  that  removing  the 
decimal  point  in  the  principal  three  places  to  the  left  gives  the 
interest  for  6  da.  at  Of/c 


306  PRACTICAL   BUSINESS   ARITHMETIC 

372.   Example.    What  is  the  interest  on  |420  for  8  da.  at 

6%? 

Solution-.     Removing  the  decimal  point  three  places  to  the  left  gives  "' 

the  interest  for  6  da.,  or  $0.42.     Since  8  da.  is  G  da.  plus  }  of  itself,         '^^^ 
$0.42  increased  by  I  of  itself,  or  $0.56  is  the  required  interest.     In  the      $.56 
following  exercises    determine  the  separate   interests  mentally  whenever  it  is 
possible  to  do  so. 

WRITTEN  EXERCISE 

1;    Find  the  total  amount  of  interest  at  6  %  on  : 
$800  for  6  da.  1720  for  6  da.  .|1500  for  6  da. 

$800  for  3  da.  1720  for  7  da.  1 1500  for  5  da. 

1800  for  2  da.  1720  for  8  da.  11500  for  4  da. 

$800  for  1  da.  $720  for  9  da.  $1500  for  9  da. 

2.  Find  the  total  amount  of  interest  at  6  %  on  : 

$1168  for  6  da.  $1600  for  6  da.  $2400  for  6  da. 

$1168  for  3  da.  $1600  for  7  da.  $2400  for  5  da. 

$1168  for  2  da.  $1600  for  8  da.  $2400  for  4  da. 

$1168  for  1  da.  $1600  for  9  da.  $2400  for  8  da. 

3.  Find  the  total  amount  of  interest  at  6  %  on  : 

$640.50  for  8  da.  $800.10  for  7  da.  $213.80  for  50  da. 

$920.10  for  20  da.  $240.80  for  90  da.  $310.40  for  40  da. 

$280.40  for  15  da.  $960.70  for  70  da.  $135.90  for  10  da. 

$390.60  for  50  da.  $845.60  for  90  da.  $736.18  for  10  da. 

ORAL    EXERCISE 

1.  600  da.  is  how  many  times  60  da.?  If  the  interest  on  $1 
for  60  da.  at  6  %  is  $0.01,  what  is  the  interest  for  600  da.? 

2.  Give  a  rapid  method  for  finding  0.1  of  a  number.  What 
is  the  interest  on  $  500  for  600  da.  at  6  %  ?  on  $  350  ?  on  $  214. 60  ? 
on  $359.80?  on  $4500?  on  $9243.80?  on  $750?  on  $2150? 

3.  What  part  of  600  da.  is  300  da.  ?  200  da.  ?  150  da.  ? 
75  da.  ?   120  da.  ?   100  da.  ?   50  da.  ? 

4.  What  is  the  interest  on  $1400  fas  600  da.  ?  for  300  da.  ? 
for  200  da.  ?  for  150  da.  ?  for  75  da.  ?  for  120  da.  ?  for  100 
da.  ?  for  50  da.  ? 


INTEREST  307 

5.  State  a  brief  method  of  finding  the  interest  for  600  da. 
at  6  %  ;  for  300  da.  ;  for  200  da.  ;  for  75  da.  ;  for  50  da.  ;  for 
150  da.  ;  for  100  da. 

6.  If  the  interest  on  11  for  600  da.  is  f  0.10,  what  is  the  inter- 
est for  6000  da.  ?  In  how  many  days  will  any  principal  double 
itself  at  6  %  interest  ? 

7.  What  is  the  interest  on  11  for  6000  da.  at  a%  ?  on  |55  ? 
on  175.60?  on  118.90?  on  1350?  on  $725?  on  19125.70. 

8.  What  is  the  interest  on  each  of  the  amounts  in  problem 
7  for  3000  da.  ?  for  2000  da.  ?  for  1000  da  ?  for  1500  da.  ? 

9.  What  is  the  interest  on  $2500  for  6000  da.?  on  $2150? 
on  17500  ?  on  $790  ?  on  $155.60? 

10.  What  is  the  interest  on  each  of  the  amounts  in  problem 
9  for  6  da.  ?  for  60  da.  ?  for  600  da  ? 

373.  In  the  above  exercise  it  is  clear  that  removing  the  deci- 
mal point  in  the  principal  one  place  to  the  left  gives  the  interest 
for  600  da.  at  6fJo  J  (^Iso  that  any  sum  of  money  will  double  itself 

in  6000  da,  at  6%. 

WRITTEN  EXERCISE 

Find  the  interest  at  6%  on : 

1.  $240  for  3000  da.  5.  $7420.50  for  600  da.   9.  $1640  for  150  da. 

2.  $318  for  6000  da.  6.  $67218.90  for  30  da.  10.  $1260. 60  fori  da. 

3.  $912  for  2000  da.  7.  $8400.50  for  400  da.  ii.  $17890  for  10  da. 

4.  $316  for  1500  da.  8.  $7500.79 for  1500  da.  12.  $1696  for  100  da. 

ORAL  EXERCISE 

1.  How  many  times  is  6  da.  contained  in  18  da.  ?  in  24  da.  ? 
in  36  da.  ?  in  42  da.  ?  in  54  da.  ?  in  48  da.  ? 

2.  What  is  the  interest  on  $150  for  6  da.  ?  for  18  da.  ?  for 
48  da.  ?  for  54  da.  ?  for  36  da.  ?  for  42  da.  ?  for  12  da.  ? 

3.  What  is  the  interest  on  $350  for  60  da.  ?  for  180  da.  ? 
for  240  da.  ?  for  360  da.  ?  for  420  da.  ?  for  480  da.  ? 

374.  Example.     Find  the  interest  on  $375  for  48  da.  at  6  %. 

Solution.  Zl\f  equals  the  interest  for  6  da.  48  da.  is  8  times  ""^^'^"^ 
6  da.     Therefore,  the  interest  for  48  da.  is  8  times  37|^,  or  $3.  $3,000 


308  PRACTICAL    BUSINESS   ARITHMETIC 


WRITTEN    EXERCISE 

1.  Find  the  total  amount  of  interest  at  6  %  on: 

1750  for  6  da.  1750  for  36  da.  $750  for  60  da. 

$750  for  12  da.  $750  for  42  da.  $750  for  180  da. 

$750  for  18  da.  $750  for  48  da.  $750  for  240  da. 

2.  Find  the  total  amount  of  interest  at  6%  on: 

$725  for  18  da.  '  $690  for  6  da.  $450  for  540  da. 

$824  for  36  da.           $129  for  60  da.  $727  for  180  da. 

$729  for  42  da.           $475  for  600  da.  $286  for  240  da. 

$850  for  54  da.           $8600  for  54  da.  $429  for  420  da. 

3.  Find  the  total  amount  of  interest  at  6  %  on: 
$317.40  for  240  da.    $217.18  for  18  da.      $360.40  for  24  da. 
$218.60  for  180  da.    $420.50  for  24  da.      $860.50  for  48  da. 
$419.80  for  420  da.    $240.70  for  540  da.    $900.60  for  66  da. 
$425.60  for  120  da.    $290.60  for  180  da.    $400.80  for  84  da. 

375.  In  some  cases  it  is  advisable  to  find  the  interest  on  the 
principal  for  1  da.  and  then  multiply  by  the  number  of  days. 

ORAL  EXERCISE 

1.  What  is  the  interest  on  $600  for  17  da.  at  6  %  ? 

Solution.     The  interest  for  one  day  is  .000^  of  the  principal,  or  10)^.     The 
interest  for  17  da.  is  17  times  10  j*,  or  $1.70. 

2.  What  is  the  interest  on  $6000  for  49  da.  at  6fo?  on  $300? 
on  $240?  on  $3000?  on  $1800?  on  $840?  on  $600? 

3.  State  the  interest  at  6^  on: 

a.  $600  for  19  da.  e.  $6000  for  37  da.  ^.  $   900  for    17  da. 

h.  $300  for  37  da.  /.  $3000  for  43  da.  j.  $1500  for    40  da. 

c.  $240  for  43  da.  ^.  $2400  for  67  da.  k,  $   600  for  139  da. 

d.  $180  for  27  da.  h.  $1800  for  89  da.  L  $  300  for  179  da. 

376.  Frequently  it  is  well  to  mentally  divide  the  days  into 
convenient  parts  of  6  or  60. 

Thus,  97  da.  =  60  da.  +  30  da.  +6  da.  +  1  da. ;   71  da.  =  60  da.  +  10  da. 
+  1  da. ;  49  da.  =  8  times  6  da.  +  1  da. 


INTEREST  309 


ORAL  EXERCISE 


Separate  the  days  in  the  following  exercise  into  6  da.  or  60  da.^ 
or  into  convenient  parts  of  6  da.  or  60  da. 

1.  8  da.  7.      7  da.  13.    86  da.  19.    17  da. 

2.  67  da.  8.  22  da.  14.    55  da.  20.    25  da. 

3.  27  da.  9.  11  da.  15.    84  da.  21.    85  da. 

4.  13  da.         10.  63  da.  16.    14  da.  22.    89  da. 

5.  72  da.         11.  37  da.  17.    97  da.  23.    19  da. 

6.  43  da.         12.  23  da.  18.    99  da.  24.    29  da. 
377.    Examples,  l.    Find  the  interest  on  1840  for  31  da.  at 

6%. 

a.  Q     Ar\ 

Solution.     31  da.  =  30  da.  +  1  da.     The   interest  for  60   da.   is      '- — '- 

$8.40  and  for  30  da.  \  of  this  sum  or  §4.20.     The  interest  for  6  da.  is  ^4.20 

$0.84  and  for  1  da.  \  of  this  sum  or  $0.14.     Adding  $4.20  and  $0.14  .14 

the  result  is  the  required  interest,  or  $ 4.34.  S4~'34 

2.    What  is  the  interest  on  12500  for  121  da.  at  6  %  ? 

Solution.     121  da.  =  2  x  60  da.  +  1  da.     The  interest  for  60  da.  ^^^-^^ 

is  $25  and  for  120  da.  twice  this  sum,  or  $50.     The  interest  for  6  ^50.00 

da.  is  $2.50  and  for  1  da.  J  of  this  sum,  or  $0.42.     Adding  $50  and  42 

$0.42  the  result  is  $50.42,  the  required  interest.  *  ^0  d9 

WRITTEN  EXERCISE 


Find  the  interest : 

Principal 

Time 

Rate 

Principal 

Time 

Rate 

1.    8420 

3  mo. 

6% 

11. 

8450 

4  mo. 

Hfo 

2.    8650 

4  mo. 

6% 

12. 

8600 

2  mo. 

Sfo 

3.    8360 

92  da. 

.4% 

13. 

8720 

8  mo. 

3% 

4.    8250 

30  da. 

3% 

14. 

8840     . 

2  mo. 

Hfo 

5.    8380 

24  da. 

1% 

15. 

8120 

7  mo. 

6% 

6.    8900 

55  da. 

6% 

16. 

8280 

9  mo. 

3-1% 

7.   8550 

47  da. 

3% 

17. 

8885.90 

20  da. 

3% 

8.    8800 

29  da. 

5% 

18. 

8240.00 

21  da. 

6% 

9.   8400 

90  da. 

4% 

19. 

8420.18 

25  da. 

mo 

10.    8270 

11  da. 

1% 

20. 

8560.17 

27  da. 

6%. 

310  PRACTICAL   BUSINESS   ARITHMETIC 

378..  It  has  been  observed  that  6  times  $800  =  800  times  16  ; 
that  0.01  of  $715  =  715  times  $0.01 ;  etc.     Hence, 

379.  The  principal  in  dollars  and  the  time  in  days  may  he 
interchanged  without  affecting  the  amount  of  interest, 

380.  Example.    Find  the  interest  on  $600  for  179  da.  at  6  %. 

Solution.  $600  for  179  da.  =  $179  for  600  da.  ;  J^  of  the  principal  equals 
the  interest  for  600  da. ;  j^  of  $  179  =  $  17.90,  the  required  interest. 

ORAL  EXERCISE 

State  the  interest  at  6  %  on : 

1.  $60  for  27  da.  11.    $360  for  91  da. 

2.  $30  for  13  da.  12.    $420  for  87  da. 

3.  $20  for  171  da.  13.    $540  for  21  da. 

4.  $10  for  186  da.  14.    $660  for  37  da. 

5.  $15  for  145  da.  15.    $750  for  56  da. 

6.  $12  for  179  da.  16.    $3600  for  218  da. 

7.  $10  for  131  da.  17.    $2000  for  183  da. 

8.  $100  for  120  da.  18.    $1200  for  155  da. 

9.  $200  for  189  da.  19.    $1800  for  181  da. 
10.    $150  for  192  da.                       20.    $2400  for  218  da. 

381.  $1500  on  interest  for  24  da.  at  8  %  =  $2000  ($1500  +  i 
of  itself)  on  interest  for  24  da.  at  6  %,  or  $1500  on  interest  for 
32  da.  (24  da.  +  J  of  itself)  at  6  %.     Hence, 

,382.  If  either  the  principal  or  the  time  is  increased  or  decreased 
by  any  fraction  of  itself  the  interest  is  increased  or  decreased  by 
the  same  fraction. 

383.  Examples,  l.  Find  the  interest  on  $  480  for  279  da. 
at  71-  %. 

Solution.  7^  %  is  i  more  than  6  %.  Increase  the  principal  by  l  of  itself,  and 
the  result  is  $600.  Interchanging  dollars  and  days,  the  problem  is  "Find  the 
interest  on  $279  for  600  da."  Pointing  off  one  place  in  the  new  principal,  the 
result  is  $27.90,  the  required  interest. 

2.    Find  the  interest  on  $2795.84  for  80  da.  at  41%. 

Solution.  4|%  is  i  less  than  6%  interest.  80  da.  decreased  by  i  of  itself 
equals  60  da.    The  interest  on  f  2795.84  for  60  da.  =  $27.96,  the  required  result. 


Interest  311 

ORAL  EXERCISE 

State  the  interest  on  : 

1.  1279.86  for  45  da.  at  4  %.  6.  12400  for  39  da.  at  5  %. 

2.  -1478.65  for  45  da.  at  4  %.  7.  12700  for  37  da.  at  4  %. 

3.  1769.64  for  48  da.  at  7 J  %.  8.  $2400  for  87  da.  at  ^  %. 

4.  1217.49  for  80  da.  at  4|  %.  9.  f  1600  for  95  da.  at  41  %. 

5.  1767.53  for  80  da.  at  4|  %.  lo.  $3200  for  59  da.  at  4^  %. 

The  Six  Per  Cent  Method 

384.  This  method  is  best  adapted  to  finding  the  interest 
when  the  time  is  one  year^  or  more  than  one  year. 

ORAL  EXERCISE 

1.  If  the  interest  on  f  1  for  1  yr.  Q.t  Q^o  is  $0.06,  what  is  the 
interest  on  $  1  for  2  yr.  ?  for  3  yr.  ?  for  4  yr.  ?  for  6  yr.  ?  for 
8  yr.  ?  for  10  yr.  ? 

2.  If  the  interest  on  $1  for  1  yr.  at  6%  is  $0.06,  what  is  the 
interest  on  $1  for  1  mo.?  for  2  mo.  ?  for  3  mo.  ?  for  6  mo.? 
for  10  mo.  ?  for  7  mo.  ?  for  8  mo.  ? 

3.  What  is  the  interest  on  $1  for  1  yr.  6  mo.  at  6%?  for 
2  yr.  6  mo.  ?  for  3  yr.  4  mo.  ?  for  3  yr.  6  mo.  ?  for  4  yr.  8 
mo.  ?  for  1  yr.  10  mo.  ?  for  5  yr.  6  mo.  ?  for  2  yr.  9  mo.  ? 

4.  What  is  the  interest  on  $50  for  1  yr.  at  6  %  ?  for  1  yr. 
6  mo.  ?  for  2  yr.  ?  for  3  yr.  6  mo.  ?  for  2  yr.  8  mo.  ?  for  1  yr. 
10  mo.  ?  for  2  yr.  6  mo.  ?  for  4  yr.  6  mo.  ?  for  1  yr.  9  mo.  ? 

5.  If  the  interest  on  $1  for  1  mo.  at  6  %  is  $0,005  (5  mills), 
what  is  the  interest  for  1  da.  ?  for  2  da.  ?  for  3  da.  ?  for  4  da.  ? 
for  6  da.  ?  for  12  da.  ?  for  18  da.  ?  for  28  da.  ?  for  24  da.  ? 

6.  What  is  the  interest  on  $1  for  1  yr.  1  mo.  1  da.  at  6%  ? 
for  2  yr.  3  mo.  3  da.  ?  for  1  yr.  10  mo.  6  da.  ?  for  4  yr.  4  mo. 
24  da.  ?  for  1  yr.  5  mo.  12  da.  ?  for  2  yr.  1  mo.  1  da.  ? 

385.  In  the  above  exercise  it  is  clear  that  : 

$0.06  =  interest  on  $lforl  yr.  at  6%. 
$0,005  =  interest  on  $lforl  mo.  at  6  %. 
$0.0001  =  interest  on  $l/or  1  da.  at  6%. 


312  PRACTICAL   BUSINESS   ARITHMETIC 

ORAL  EXERCISE 

Find  the  interest  on$l  at  6(fo  for: 

1.  1  yr.  4  mo.  12  da.  5.  2  yr.  6  mo.  6  da. 

2.  1  yr.  8  mo.  18  da.  6.  3  yr.  4  mo.  9  da. 

3.  1  yr.  7  mo.  24  da.  7.  5  yr.  3  mo.  3  da. 

4.  1  yr.  9  mo.  27  da.  8.  4  yr.  8  mo.  4  da. 
Find  the  interest  at  6%  on: 

9.    1250  for  2  yr.  14.    1350  for  3  yr. 

10.  1400  for  5  yr.  15.    $450  for  2  yr.  3  mo. 

11.  1700  for  4  yr.  16.    $150  for  1  yr.  6  mo. 

12.  1300  for  3  yr.  4  mo.  17.    150  for  1  yr.  2  mo.  6  da. 

13.  $500  for  4  yr.  2  mo.  18.    $10  for  2  yr.  6  mo.  6  da. 
386.   Example.    What  is  the  interest  on  $600  for  2  yr.  8  mo. 

15  da.  at  6  %  ? 

Solution.    Find  the     $0.12        =  int.  on  $1  for  2  yr. 
interest  on  $1  for 2  yr.;  ^^        ^    .^^^^  ^^^  ^^  ^^^  g  ^^^^ 

on  $1   for  8  mo.;    on  r^r^r^r         •  ^t    i<       -»       ^ 

$1  for  15  da.    The  sum  -Q^^^  =  int.  on  $1  for  15  da. 

of  these  interest  items  $0.1625  =  int.  on  $1  for  the  given  time. 

equals  ^0.1625,  the  in-  600  X  $0.1625  =  $97.50,  int.  on  $600 

terest    on    ^  1    for    the  j-       o  o  icj         t.  a  nt 

\„.,     -^  ,  lor  2  yr.  8  mo.  15  da.  at  6%. 

given  time  at  6%.    Mul-  "^  ' 

tiplying  this  interest  by  the  given  number  of  dollars,  600,  the  product  is  the 
required  interest,  $97.50.     Change  to  any  other  rate  as  in  §  362. 

Sometimes  it  is  shorter  to  find  the  interest  on  $  1  for  the  given  time  at 
any  given  rate,  and  multiply  by  the  number  of  dollars  in  the  principal. 
Thus  to  find  the  interest  on  $400  for  2  yr.  6  mo.  at  8%,  take  400  times  20^ 
(2^  X  8^)  ;  on  $500  for  5  yr.  3  mo.  at  4%,  take  500  times  21  f  (5^  x  8;?)  ; 
on  $600  for  1  yr.  9  mo.  at  4%  take  600  times  lf\  etc. 


ORAL  EXERCISE 

Find  the  interest : 

Principal 

Time 

Rate 

Principal 

Time 

Rate 

1.    $400 

1  yr.  2  mo. 

6% 

7.   $840 

1  yr.  6  mo. 

6% 

2.   $500 

2  yr.  4  mo. 

6% 

8.    $100 

3  yr.  6  mo. 

5% 

3.   $300 

4  yr.  6  mo. 

6% 

9.   $960 

4  yr.  2  mo. 

6% 

4.   $250 

1  yr.  8  mo. 

6% 

10.   $300 

3  yr.  4  mo. 

3% 

5.   $200 

2  yr.  10  mo. 

3% 

11.   $240 

2  yr.  6  mo. 

4% 

6.   $300 

1  yr.  11  mo. 

6% 

12.   $180 

1  yr.  8  mo. 

6% 

.      INTEREST  313 

WRITTEN  EXERCISE 

Find  the  interest: 

1.  Principal,  f74.90;  time,  6  mo.  15  da.  ;  rate,  4%. 

2.  Principal,  1986.00;  time,  11  mo.  28  da.;  rate,  4-|  %. 

3.  Principal,  11900.00;  time,  10  mo.  28  da.;  rate,  6%. 

4.  Principal,  $87.55;  time,  4  yr.  5  mo.  6  da.;  rate,  6%. 

5.  Principal,  f  735.00;  time,  4  yr.  4  mo.  4  da.;  rate,  6%. 

6.  Principal,  $609.50;  time,  2  yr.  7  mo.  6  da.;  rate,  6%. 

7.  Principal,  $875.40;  time,  1  yr.  2  mo.  21  da.;  rate,  41%. 

8.  Principal,  11124.75;  time,  1  yr.  5  mo.  14  da.;  rate,  6%. 

9.  Principal,  $1245.00  ;  time,  3  yr.  6  mo.  23  da. ;  rate,  6  %. 
10.  Principal,  $1570.00;  time,  1  yr.  9  mo.  25  da.;  rate,  5%. 

The   Reference  Method 

387.  This  method  employs  a  series  of  tables  in  which  inter- 
est computations  are  already  worked  out,  and  by  the  use  of 
which  the  interest  may  be  found  on  any  sum,  at  given  rates, 
for  any  time. 

This  method  is  used  in  banks,  insurance  offices,  and  kindred  institutions, 
and  it  greatly  lessens  the  work  of  computing  interest.  Many  different  sys- 
tems are  published,  but  the  section  of  an  interest  table  given  on  page  314 
will  illustrate  the  general  plan  followed. 

ORAL  EXERCISE 

1.  What  is  the  interest  (use  the  table,  page  314)  on  $8  for 
5  da.?  on  $80?  (10  x  $8);  on  $800?  on  $8000? 

2.  What  is  the  interest  on  $10  for  7  da.?  on  $100?  on 
$1000  ?  on  $10,000?  on  $70  for  5  da.?  on  $700  ?  on  $7000  ? 

3.  What  is  the  interest  on  $4  for  11  mo.  ?  on  $40  for  the 
same  time?  on  $400?  on  $4000?  on  $50,000  for  7  mo.  ? 

388.  Example.    Find  the  interest  on  $9980  for  7  da.  at  6%. 

Solution  :    By  the  table,  $  10.50  =  interest  on  $  9000. 

1.05  =  interest  on    $900. 

.09  =  interest  on      $  80. 

$11.64  =  interest  on  $  9980.. 


314 


PRACTICAL   BUSINESS  ARITHMETIC 


Interest  Table 

AT  6% 

Time 

$1 

$2 

$3 

$4 

$5 

$6 

$7 

$8 

$9 

$10 

Time 

1  da. 

.00017 

.00033 

.0005 

.00067 

.00083 

.001 

.00117 

.00133 

.0015 

.00167 

Ida. 

2  da. 

.00033 

.00067 

.001 

.00133 

.00167 

.002 

.00233 

.00267 

.003 

.00333 

2  da. 

8  da. 

.0005 

.001 

.0015 

.002 

.0025 

.003 

.0035 

.004 

.0045 

.005 

3  da. 

4  da. 

.00067 

.00133 

.002 

.00267 

.00333 

.004 

.00467 

.00533 

.006 

.00667 

4  da. 

5  da. 

.00083 

.00167 

.0025 

.00333 

.00417 

.005 

.00583 

.00667 

.0075 

.00883 

5  da. 

6  da. 

.001 

.002 

.003 

.004 

.005 

.006 

.007 

.008 

.009 

.01 

6  da. 

7  da. 

.00117 

.00233 

.0035 

.00467 

.00583 

.007 

.00817 

.00933 

.0105 

.01167 

7  da. 

8  da. 

.00133 

.00267 

.004 

.00533 

.00667 

.008 

.00983 

.01067 

.012 

.0133 

8  da. 

9  da. 

.0015 

.003 

.0045 

.00667 

.0075 

.009 

.0105 

.012 

.0135 

.015 

9  da. 

10  da. 

.00167 

.00333 

.005 

.00667 

.00833 

.01 

.01167 

.01333 

.015 

.01667 

10  da. 

20  da. 

.00333 

.00667 

.01 

.01333 

.01667 

.02 

.02333 

.02667 

.03 

.03333 

20  da. 

1  mo. 

.005 

.01 

.015 

.02 

.025 

.03 

.035 

.04 

.045 

.05  • 

1  mo. 

2  mo. 

.01 

.02 

.03 

.04 

.05 

.06 

.07 

.08 

.09 

.10 

2  mo. 

3  mo. 

.015 

.03 

.045 

.06 

.075 

.09 

.105 

.12 

.135 

.15 

3  mo. 

4  mo. 

.02 

.04 

.06 

.08 

.10 

.12 

.14 

.16 

.18 

.20 

4  mo. 

5  mo. 

.025 

.05 

.075 

.10 

.125 

.15 

.175 

.20 

.225 

.25 

5  mo. 

6  mo. 

.03 

.06 

.09 

.12 

.15 

.18 

.21 

.24 

.27 

.80 

6  mo. 

7  mo. 

.035 

.07 

.105 

.14 

.175 

.21 

.245 

.28 

.315 

.35 

7  mo. 

8  mo. 

.04 

.08 

.12 

.16 

.20 

.24 

.28 

.32 

.36 

.40 

8  mo. 

9  mo. 

.045 

.09 

.135 

.18 

.225 

.27 

.315 

.36 

.405 

.45 

9  mo. 

10  mo. 

.05 

.10 

.15 

.20 

.25 

.30 

.35 

.40 

.45 

.50 

10  mo. 

11  mo. 

.055 

.11 

.165 

.22 

.275 

.33 

.385 

.44 

.495 

.55 

11  mo. 

1  yr. 

.06 

.12 

.18 

.24 

.80 

.36 

.42 

.48 

.54 

.60 

lyr. 

2yr. 

.12 

.24 

.36 

.48 

.60 

.72 

.84 

.96 

1.08 

1.20 

2yr. 

WRITTEN  EXERCISE 

Using  the  tahle^  find  the  interest  on  : 

1.  $8800  for  4  da.         ^       5.   117,000  for  1  da. 

2.  19600  for  5  da.  6.   $29,000  for  1  da. 

3.  $7500  for  7  mo.  7.   $71,000  for  7  da. 

4.  $8500  for  11  mo.  8.   $87,000  for  11  da. 


PROMISSORY  NOTES 

389.    A  written  promise  to  pay  a  certain  sum  of  money  on 
demand,  or  at  a  specified  time,  is  called  a  promissory  note. 


%^2jAI. 


New  York,. 


X- 


-19- 


■Z^i^y-r7^.<yy?^<h^ 


^ 


of     ~^J^,^f^J^..^^^'''^Xr<^^ 


.after  date_ 


^ 


promise  to  pay  to 


the  order 


'^^^  - 


JDollars 


Value  received 
Ho.  ^4^  Due     y^/ 


^>/g^;^; 


S:i^Z= 


INTEREST 


315 


390.  In  the  foregoing  note  Ellis  B.  Pitkin  is  the  maker ; 
William  B.  Harris,  the  payee ;  and  1243.50,  the  face.  The  note 
is  negotiable  ;  that  is,  it  may  be  transferred  by  the  payee  to 
any  other  person  by  indorsement. 

If  the  note  were  drawn  payable  to  William  B.  Harris,  or  hearer,  it  would 
be  transferable  by  delivery  and  would  be  negotiable.  If  the  words  to  the 
order  of  were  omitted,  the  note  would  not  be  transferable  either  by  indorse- 
ment or  by  delivery ;  it  would  be  payable  to  William  B.  Harris  only,  and 
would  be  called  a  non-negotiable  note. 

391.  If  the  payee  should  sell  the  foregoing  note,  he  would 
have  to  indorse  it;  that  is,  make  it  payable  to  the  buyer  by  a 
writing  on  the  back  of  the  instrument.  This  indorsement  may 
be  made  in  either  of  the  three  ways  shown  in  the  margin. 

William  B.  Harris  sold  the  note  to  O.  D.  Merrill  and  effected  the  transfer 
by  a  blank  indorsement.  This  is  simply 
William  B.  Harris's  signature.  It  makes 
the  note  payable  to  bearer.  O.  D.  Merrill 
sold  the  note  to  Andrew  J.  Lloyd  and 
effected  the  transfer  by  a  full  indorsement, 
an  indorsement  which  specifies  the  one  to 
whose  order  the  note  is  made  payable.  By 
indorsing  the  note  both  William  B. 
Harris  and  O.  D.  Merrill  make  themselves 
responsible  for  its  payment  in  case  the 
maker  does  not  pay  it.  O.  H.  Briggs  was 
willing  to  buy  the  note  without  Andrew  J. 
Lloyd's  guarantee  to  pay  it.  The  transfer 
was  effected  by  a  qualified  indorsement. 
By  this  indorsement  Andrew  J.  Lloyd  avoids 
the  responsibility  of  an  ordinary  indorser. 

The  note  just  considered  is  a  time  note; 
if  the  words  On  demand  were  substituted 
for  the  words  Two  months  after  date  the  form 
would  be  called  a  demand  note.  The  note 
is  interest-bearing  because  it  contains  a 
clause  to  that  effect ;  it  would  draw  interest 
after  it  became  due  without  any  interest 
clause.  A  demand  note,  in  which  there  is 
no  interest  clause,  draws  interest  after  payment  has  been  demanded. 


Blank  Indorisement 


Full  Indorsement 


':^^.^^t(7::^t:d.^^i;y'^p^^■■■d^c 


Qualified  lndor$ement 


316  PRACTICAL   BUSINESS   ARITHMETIC 

392.  A  note  in  which  two  or  more  persons  jointly  and 
severally  promise  to  pay  is  called  a  joint  and  several  note;  a 
note  in  which  two  or  more  persons  jointly  promise  to  pay,  a 
joint  note. 

%.:3j2J2:==r  Rochester,  N.Y.,_^ uC 19 

.'       "        ^~r::^Z-i>iP:<C-Y'-^2^>^^^r<^  '''•-  -'        —after  date  we  jointly  and  severally  promise  to 

pay tojjhe^order  of ^^,  //f .V?.^rP-^  ^^^-k'^^T?-^^ -   — - — ■         ■  _ 

—    -  Dnllars 


^^^^^  yp/^^-^^^^^  "^/if- 


Payable  a«- --r<^'^^^-'T^7S/^^^  yZ^^^€y-7<r.^^''y\X^.^^^ 


Value  received 


Nn.   .^     rhir>(^^4fy^  ^O^/r^J^^^^n^. 


lu  a  joint  and  several  note,  the  holder  may  sue  and  collect  of  any  one  signer 
without  proceeding  against  the  others,  or  he  may  sue  all  of  them  together. 
In  a  joint  note  the  signers  must  be  sued  jointly.  The  distinction  between 
a  joint  and  a  joint  and  several  note  has  been  abolished  by  law  in  many  of 
the  states.  The  above  form  is  a  joint  and  several  note.  If  the  words  and 
severally  were  omitted  it  would  be  a  joint  note. 

The  words  value  received  in  a  note  are  equivalent  to  an  acknowledgment 
that  there  has  been  a  consideration.  Their  insertion  is  usual  and  advisable, 
but  not  legally  required  in  all  the  states 

WRITTEN  EXERCISE 

Write  interest-hearing  notes  as  follows : 

1.  A  demand  note;  amount,  11283.97  ;  current  date;  payee, 
C.  H.  Good;  maker  (your  name);  interest  at  5|^. 

2.  A  time  note  ;  amount,- 1 728.79  ;  current  date  ;  time,  90  da. ; 
payee.  Snow  &  Co.;  maker  (your  name);  interest  at  3|  ^. 

3.  A  joint  note;  amount,  11795.73;  current  date;  time,  6 
mo.;  payee,  Ellis  &  Co.;  maker  (your  name),  and  Richard 
Roe ;  interest  at  4|/o.  Write  a  joint  note  under  the  same  con- 
ditions. 

4.  Find  the  amount  (face  plus  interest)  due  87  da.  after  date 
in  note  No.  1;  at  the  end  of  the  time  in  note  No.  2;  at  the 
end  of  the  time  in  note  No.  3. 


INTEREST  B17 

EXACT   INTEREST 

393.  Exact  interest  is  simple  interest  for  tlie  exact  number  of 
days  on  the  basis  of  365  da.  in  a  common  year,  or  366  da.  in  a 
leap  year. 

The  United  States  Government  takes  exact  interest,  and  its  use  is 
growing  among  business  men.  In  strict  justice  it  is  the  only  correct 
method  of  computing  interest. 

394.  The  difference  between  the  common  year  of  365  da. 
and  the  commercial  year  of  360  da.  is  5  da.,  or  yig  of  the  com- 
mon year. 

If  any  sum  were  divided  into  360  parts,  each  part  would  be  larger  than  it 
would  be  if  the  sum  were  divided  into  36.5  parts.  Thus,  -^^^  and  -^^\  are 
greater  than  gV^  and  -^^^.  It  is  therefore  clear  that  exact  interest  is  less  than 
ordinary  interest. 

395.  To  find  the  exact  interest,  compute  interest  in  the  usual 
way  for  the  commercial  year,  and  from  the  interest  thus  obtained 
subtract  y^^  of  itself 

In  many  cases  the  work  may  be  shortened  by  cancellation. 

396.  Example.    Find  the  exact  interest, on  13285  for  35  da. 

at  5%. 

9 
Solution.    :2^^i-§^AlMf  =  .05x35 x  $9  =  $15.76. 

m 

WRITTEN  EXERCISE 

Find  the  exact  interest : 

1.  1734.50  for  124  da.  at  6  %.  7.  $1240.35  for  50  da.  at  6%. 

2.  1420.60  for  99  da.  at  ^%.  8.  11630.25  for  67  da.  at  4  %. 

3.  $965.50  for  82  da.  at  ^  %.  9.  $150,000  for  28  da.  at  6%. 

4.  $356.40  for  236  da.  at  4%.  10.  $100,000  for  135  da.. at  5%. 

5.  $672.50  for  53  da.  at  5^  %.  ii.  $4653.28  for  182  da.  at  4%. 

6.  $546.24  for  38  da.  at  41  %.  12.  $45,000  for  42  da.  at  21%. 

13.  $3500  from  July  17,  1916,  to  Nov.  26, 1916,  at  3%  ;  at  4i%. 

14.  S2315.89fromMar.  11,  1916,toSept.l,1916,at6%;  at  2%. 

15.  S872.54  from  Oct.  18, 1915,  to  Jan.  16, 1916,  at  5%  ;  at  71%. 

16.  X1006  68.  from  Apr.  1,  1916,  to  Yob.  19, 1917,  at  3%  ;  at  2%. 


318  PRACTICAL  BUSINESS  ARITHMETIC 

PROBLEMS  IK   INTEREST 


ORAL 

EXERCISE 

Principal 

Interest 

Time 

Rate 

Amount 

1. 

$200 

$24 

2yr. 

? 

? 

2. 

S250 

$30 

? 

3% 

? 

3. 

$240 

$30 

? 

5^^, 

? 

4. 

$320 

? 

3  yr. 

5% 

? 

5. 

? 

$54 

Syr. 

6% 

? 

6. 

$450 

$45 

2yr. 

? 

9 

7. 

$525 

? 

4yr. 

2% 

? 

8. 

? 

$84 

3-1  yr. 

6% 

? 

9. 

? 

? 

3yr. 

4% 

$112 

10. 

$225 

$36 

4  yr. 

? 

? 

11. 

$625 

? 

^  yr. 

4% 

? 

12. 

? 

$52.50 

? 

3% 

$402.50 

13. 

If  the  cash 

price  of  an 

article  is 

$125,  what  will  be  the 

sixty-day  credit  price  if  money  is  worth  6  %  ? 

Suggestion.  The  cash  price  plus  the  interest  for  the  given  time  at  the 
given  rate  equals  the  credit  price. 

14.  If  the  thirty -day  credit  price  of  an  article  is  $50.25,  what 
will  be  the  cash  price  if  money  is  worth  6  %  ? 

Suggestion.  The  credit  price  divided  by  the  amount  of  one  dollar  for 
the  given  time  at  the  given  rate  equals  the  cash  price. 

15.  If  the  cash  price  of  an  article  is  $240.50,  what  will  be  the 
sixty-day  credit  price  if  money  is  worth  6  %  ? 

16.  If  the  four  months  credit  price  of  an  article  is  $163.20, 
what  will  be  the  cash  price  if  money  is  worth  6  %  ? 

17.  If  the  cash  price  of  an  article  is  $265.50,  what  will  be  the 
sixty -day  credit  price  if  money  is  worth  6  %  ? 

18.  If  the  cash  price  of  an  article  is  $210,  what  will  be  the 
sixty-day  credit  price  if  money  is  worth  4  %  ? 

19.  One  contractor  offers  to  do  a  certain  piece  of  work  for 
$425.50  cash;  another  offers  to  do  the  same  work  for  $441, 
payable  in  1  yr.    If  money  is  worth  5  %,  which  is  the  better  offer  ? 


INTEREST  319 

WRITTEN  EXERCISE 

1.  Which  is  the  better  for  a  tailor,  to  sell  a  suit  for  $65  cash, 
or  for  $73.15  on  9  mo.  time,  money  being  worth  6%  ? 

2.  Which  is  the  better,  to  sell  carpet  at  $1.50  per  yard  cash, 
or  at  $1.68  per  yard  on  1  yr.  time,  money  being  worth  5%  ? 

3.  Which  is  the  more  advantageous,  to  buy  an  article  for 
$58.50  cash  or  for  $61.80  on  6  mo.  time,  money  being  worth 
6%? 

4.  A  merchant  paid  $160  cash  for  4  sewing  machines.  After 
keeping  them  in  stock  1  yr.  6  mo.  he  sold  them  for  $190.80, 
on  one  year's  time  without  interest.  If  money  is  worth  6%  what 
was  his  gain  or  loss  at  the  time  of  the  sale  ? 

5.  An  invoice  of  merchandise  listed  at  $2500,  on  which  trade 
discounts  of  20%  and  10%  were  allowed,  was  purchased  at  90 
da.  What  was  the  actual  cash  value  of  the  debt  on  the  day 
of  the  purchase,  money  being  worth  5%  ? 

6.  A  merchant  bought  600  bbl.  of  flour  at  $7.50  per  barrel. 
Terms:  one  half  on  account,  3  mo.;  one  half  on  account,  6  mo. 
At  the  end  of  1  mo.  he  paid  the  cash  value  of  the  entire  bill. 
How  much  did  he  gain,  money  being  worth  6%? 

7.  Sept.  8  you  purchased  of  Edward  Sprague  &  Son,  at  trade 
discounts  of  20%  and  25%,  an  invoice  of  coffee  listed  at  $2006. 
Terms :  30  da.  Sept.  20  you  sent  Edward  Sprague  &  Son  a 
check  for  the  actual  cash  value  of  the  bill.  What  was  the 
amount  of  the  check,  money  being  worth  6%? 

PERIODIC   INTEREST 

397.  Periodic  interest  is  simple  interest  on  the  principal 
increased  by  the  simple  interest  on  each  installment  of  interest 
that  was  not  paid  when  due. 

As  periodic  interest  can  be  legally  enforced  in  only  a  few  states,  special 
contracts  should  be  made  if  it  is  to  be  collected.  Where  technically  illegal, 
periodic  interest  is  often  collected ;  as,  when  a  series  of  notes  is  given  for 
the  interest  on  a  note  secured  by  a  real-estate  mortgage,  such  notes  to  draw 
interest  if  not  paid  when  due. 


320  PRACTICAL   BUSINESS   ARITHMETIC 

398.    Example.    If  payments  of  interest  are  due  semiannually, 
what  is  the  interest  on  flOOO  for  3  yr.  at  6%  ? 

Solution 

$  180       =  interest  on  $  1000  for  3  yr.  at  6%. 

f  30  is  the  interest  on  $  1000  for  one  semiannual  period,  6  mo. 

1st  installment  of  interest,  $30,  was  unpaid  for  2  yr.  6  mo. 

2d  installment  of  interest,  f  30,  was  unpaid  for  2  yr. 

3d  installment  of  interest,  $  30,  was  unpaid  for  1  yr.  6  mo. 

4th  installment  of  interest,  $  30,  was  unpaid  for  1  yr. 

5th  installment  of  interest,  f  30,  was  unpaid  for  6  mo. 

The  sum  of  the  periods  for  which  interest  was  unpaid  is     7  yr.  G  mo. 

The  interest  on  each  $  30  for  the  period  it  was  unpaid  is  the  same  as 

the  interest  on  $  30  for  the  sum  of  the  periods. 
13.50  -  interest  on  $30  for  7  yr.  G  mo.,  at  6%. 
$193.50  =  the  total  interest  due. 

WRITTEN    EXERCISE 

1.  If   payments    of  interest   are  due  annually,  what  is  the 
interest  on  f  850  for  5  yr.,  at  8  %  ? 

2.  If  payments  of   interest  are  due  quarterly,  what  is    the 
interest  on  11380  for  2  yr.  6  mo.,  at  4%? 

3.  What  is  the  difference  between  the  simple  interest  and 
periodic  interest  (payable  annually)  on  $1800  for  6  yr.  at  4%? 

4.  If   payments    of    interest    are    due    semiannually,    what 
amount  should  be  paid  in  settlement  of  a  debt  of  $1450  which, 


has  run  5  yr.  at  6%? 

5.  If  payments  of  interest  are  due  annually,  what  amount 
will  settle  a  debt  of  $1500  for  5  yr.,  at  6  %,  if  the  first  install- 
ment of  interest  was  paid  when  due  ? 

COMPOUND   INTEREST 

399.  Compound  interest  is  interest  computed,  at  certain  inter- 
vals, on  the  sum  of  the  principal  and  unpaid  interest. 

Interest  maybe  compounded  annually,  semiannually,  quarterly,  or  even 
monthly.  In  most  states  the  law  does  not  sanction  the  collection  of  com- 
pound interest,  but  if  it  is  agreed  upon  by  the  parties,  the  taking  of  it  does  not 
constitute  usury.  It  is  a  general  custom  of  savings  banks  to  allow  compound 
interest.     Compound  interest  is  also  used  by  life  insurance  companies. 


INTEKEST 


321 


400.    Example. 

for  4  yr 


What  is  the   compound   interest  on 
if  the  interest  is  compounded  annually  at  5  %  ? 


Solution.   $6000 

300 
6300 

315 
6615 

330.75 
6945.75 

347.29 

7293.04 

$7293.04 


=  1st  principal. 

=  interest  1st  year. 

=  amount,  or  the  principal  the  2d  year. 

=  interest  2d  year. 

=  amount,  or  the  principal  the  3d  year. 

=  interest  3d  year. 

=  amount,  or  the  principal  the  4th  year. 

=  interest  4th  year. 

=  amount  due  at  the  end  of  the  4th  year. 

-  $  6000  =  $  1293.04,  compound  interest  for  4  yr. 


WRITTEN  EXERCISE 

1.  If  interest  is  compounded  annually,  what  will  be  the 
amount  of  ^600  for  5  yr.  at  G  %  ? 

2.  If  interest  is  compounded  semiannually,  what  will  be  the 
compound  interest  on  $1500  for  2  yr.  6  mo.  at  4  %  ? 

3.  A  placed  $750  in  a  savings  bank  Jan.  1, 1915,  and  inter- 
est was  added  thereto  every  6  mo.  at  the  rate  of  4%.  No  with- 
drawals having  been  made,  what  was  the  balance  due  Jan.  1,1917? 

Table  Showing  the  Amounts  of  $1  at  Compound  Interest  Compounded 

Annually 


Yii. 

2% 

'4% 

3% 

H% 

4% 

4h7o 

'o% 

Yii. 

1 

1.02000 

1.02500 

1.03000 

1.0.3500 

1.04000 

1.04500 

1.05000 

1 

2 

1.04040 

1.05063 

1.06090 

1.07123 

1.08160 

1. "09203 

1.10250 

2 

3 

1.0(5121 

1.07689 

1.09273 

1.10872 

1.12486 

1.14117 

1.15763 

3 

4 

1.08243 

1.10381 

1.12551 

1.14752 

1.16986 

1.19252 

1.21551 

4 

5 

1.10408 

1.13141 

1.15;)27 

1.18769 

1.21665 

1.24G18 

1.27628 

5 

6 

1.12616 

1.15969 

1.19405 

1.22926 

1.26532 

1.30226 

1.34010 

6 

7 

1.1486:) 

1.18869 

1.22987 

1.27228 

1.. 31 593 

1.36086 

1.40710 

7 

8 

1.17166 

1.21840 

1.26677 

1.31681 

1.36857 

1.42210 

1.47746 

8 

9 

1.19509 

1.21886 

1.30477 

1.36290 

1.42331 

1.48610 

1.55133 

9 

10 

1.21899 

1.2S009 

1.. 34392 

1.41060 

1.48024 

1.55297 

1.62889 

10 

11 

1.24337 

1.31209 

1.. 38423 

1.45997 

1.53945 

1.62285 

1.71034 

11 

12 

1.26824 

1. .314  89 

1.42576 

1.51107 

1.60103 

1.69588 

1.79586 

12 

13 

1.29361 

1.37851 

1.46853 

l.f;6396 

1.66507 

1.77220 

1.88565 

13 

14 

1.31948 

1.41297 

1.51259 

1.61870 

1.73168 

1.85194 

1.97993 

14 

15 

1.34587 

1.44830 

1.55797 

1.67535 

1 .80094 

1.9.3528 

2.07893 

15 

10 

1.37279 

1.48451' 

1.60171 

1.73399 

1.87298 

2.02237 

2.18287 

16 

17 

1.40024 

1.52162 

1.65285 

1.79468 

1.94790 

2.11338 

2.29202 

17 

18 

1.42825 

1.559(J6 

1.70243 

1.85749 

2.02582 

2.20848 

2.40662 

18 

19 

1.45681 

1.59865 

1.753.51 

1.92250 

2.10685 

2.30786 

2. .52695 

19 

20 

1.485% 

1.63862 

1.80611 

1.98979 

2.19112 

2.41171 

2.65330 

20 

322 


PRACTICAL   BUSINESS   ARITHMETIC 


ORAL  EXERCISE 

Refer  to  the  tahle^  page  321,  a7id  give  rapid  ansivers  to  the 
following : 

1.  What  is  the  amount  of  |1  for  12  yr.  at  4%  ?  at  8%  ?  at 
5%  ?  at  41%  ?  at  2^%  ? 

2.  What  is  the  amount  of  |1  for  18  yr.  at  4i%  ?  at  8^%  ? 
at  2%  ?  at  3%  ?  at  2|%? 

3.  What  is  the  amount  of  $1  for  9  yr.  at  5%  ?  at  4|%  ?  at 
21%  ?  at  31%  ?  at  8%  ?  at  4%  ? 

4.  What  is  the  amount  of  il  for  20  yr.  at  2%  ?  at  5%  ?  at 
41%  ?  at  31%  ?  at  21%  ?  at  3%  ? 

5.  What  is  the  amount  of  $10  for  10  yr.  at  4  %  ?  for  20  yr. 
at  2  %  ?  for  5  yr.  at  5  %  ? 

6.  What  is  the  amount  of  flOO  for  5  yr.  at  2%  ?  for  11  yr. 
at  81  %  ?  for  19  yr.  at  5  %  ? 

401.  Example.  What  is  the  compound  interest  on  $8000 
for  10  yr.,  if  interest  is  compounded  annually  at  5%  ? 

Solution.     $1.62889  =  amount  of  $1  for  10  yr.  at  5%. 

8000  X  $  1.62889  =  $13031.12,  amount  due  in  10  yr.  at  5%. 
$13031.12  -  $8000  =  $5031.12,  the  compound  interest. 

If  interest  is  compounded  semiannually,  take  one  half  the  rate  for  twice 
the  time ;  if  quarterly,  take  one  fourth  the  rate  for  four  times  the  time. 

The  table  may  be  used  for  periods  longer  than  20  yr.  For  40  yr.  multiply 
the  amount  of  $1  for  20  yr.  by  itself,  and  the  product  will  be  the  amount  for 
40  yr. ;  for  35  yr.  multiply  the  amount  of  $  1  for  20  yr.  by  the  amount  of  $1 
for  15  yr. ;  the  result  will  be  the  amount  for  35  yr. 


WRITTEN  EXERCISE 
Find  the  compound  interest  : 
Principal  Rate 

1.  $7500  4% 

2.  $2500  2% 

3.  $5600  31% 

4.  $3350  5% 

5.  ,$2875  3% 

6.  $4600  4% 


Time 

Interest  Payable 

5  yr. 

Annually 

12  yr. 

Annually 

20  yr. 

Annually 

10  yr. 

Semiannually 

17  yr. 

Annually 

15  yr. 

Semiannually 

INTEREST 


323 


Sinking   Funds 

402.  A  sinking  fund  is  a  sum  of  money  set  aside  at  regular 
intervals  for  the  purpose  of  paying  off  an  existing  or  anticipated 
indebtedness,  or  of  replacing  a  value  which  will  disappear  by 
depreciation,  exhaustion,  or  termination. 

The  payment  of  a  public  or  a  corporation  debt  and  the  replacing  of 
certain  public  and  corporate  values  are  sometimes  facilitated  by  regularly 
investing  a  certain  sum  in  some  form  of  security.  The  interest  and  prin- 
cipal from  these  investments  from  year  to  year  constitute  a  sinking  fund, 
which,  it  is  planned,  shall  accumulate  to  an  amount  sufficient  to  redeem  the 
debt  when  it  falls  due  or  replace  the  value  when  it  disappears. 

ORAL  EXERCISE 

1.  In  what  time  will  any  sum  of  money  double  itself  at  4  % 
simple  interest  ?  at  3  %  ?  at  6  ^o  ?  at  4|  %  ? 

2.  How  long  (approximately)  will  it  take  81  to  double  it- 
self at  3|  %  ?  compound  interest,  compounded  annually  ?  (See 
table,  page  321.) 

3.  How  long  (approximately)  will  it  take  any  sum  to  double 
itself  at  4|  %  compound  interest,  compounded  annually  ?  at  5  % 
compound  interest,  compounded  annually  ? 

4.  If  you  put  11  at  compound  interest  to-day,  $1  one  year 
from  to-day,  and  so  on  for  20  yr.,  how  much  would  you  have 
at  the  end  of  the  twentieth  year,  interest  being  compounded 


annually  at  4  = 


(See  table  below.) 


403.  In  the  following  table  is  shown  the  sum  to  which  f  1,  paid 
at  the  beginning  of  each  year,  will  increase  at  certain  rates  of  com- 
pound interest  in  any  number  of  years  not  exceeding  twenty. 


Ye. 

2% 

4% 

4^% 

Ye. 

2% 

4% 

4i% 

1 

1.020000 

1.040000 

1.045000 

11 

12.412089 

14.025805 

14.464031 

2 

2.060400 

2.121600 

2.137025 

12 

13.680331 

15.626837 

16.159913 

3 

3.121608 

3.246464 

3.278191 

13 

14.973938 

17.291911 

17.932109 

4 

4.204040 

4.416322 

4.470709 

14 

16.293416 

19.023587 

19.784054 

5 

5.308120 

5.632975 

5.716891 

15 

17.639285 

20.824531 

21.719336 

6 

6.434283 

6.898294 

7.019151 

16 

19.012070 

22.697512 

23.741706 

7 

7.582969 

8.214226 

8.380013 

17 

20.412312 

24.645412 

25.855083 

8 

8.754628 

9.582795 

9.802114 

18 

21.840558 

26.671229 

28.063562 

9 

9.949721 

11.006107 

11.288209 

19 

23.297869 

28.778078 

30.371432 

10 

11.168715 

12.486351 

12.841178 

20 

24.783317 

30.5)69201 

32.783136 

324  PEACTICAL   BUSINESS  AEITHMETIC 

WRITTEN  EXERCISE 

1.  At  the  beginning  of  each  year  for  10  yr.  a  certain  rail- 
road company  put  aside  out  of  the  profits  of  the  previous  year 
150,000  as  a  sinking  fund.  If  this  sum  was  invested  at  4% 
compound  interest,  compounded  annually,  what  did  it  amount 
to  at  the  end  of  the  tenth  year  ? 

2.  Jan  1,  1915,  a  certain  city  borrowed  8500,000  and  agreed 
to  pay  the  same  on  Jan.  1,  1925.  What  sum  must  be  invested 
on  Jan.  1,  1915,  and  annually  for  10  yr.,  in  securities,  paying 
4 J  %  compound  interest,  compounded  annually,  in  order  to  pay 
the  loan  when  it  becomes  due? 

3.  On  Dec.  31,  1915,  a  certain  town  borrowed  140,000  with 
which  to  build  a  new  high  school.  It  was  agreed  that  this 
amount  should  be  paid  on  Dec.  31,  1920.  What  sum  must 
the  town  set  aside  and  invest  at  41^%  compound  interest,  com- 
pounded annually,  on  Jan.  1,  1913,  and  each  year  thereafter  for 
5  yr.,  in  order  to  pay  the  debt  when  it  becomes  due? 

4.  What  sum  must  a  town  set  aside  and  invest  annually  to 
rebuild  a  bridge  costing  $30,969.20,  estimated  to  last  20  yr., 
allowing  4  %  compound  interest,  compounded  annually? 

WRITTEN   REVIEW  EXERCISE 

1.  What  amount  of  interest  (in  United  States  money)  at  6  % 
will  accrue  on  a  debt  of  X84  12s.  in  5  mo.  24  da.? 

2.  The  yearly  taxes  on  a  house  and  lot  which  cost  112,500 
are  $162.  How  much  should  the  house  rent  for  per  month 
to  clear  6  %  on  the  investment  ? 

3.  A  bought  16,000  bu.  of  wheat  at  85/,  and  paid  for  it  in 
10  da.  46  da.  from  the  date  of  purchase  he  sold  the  wheat  for  92/ 
per  bushel,  cash.     If  money  was  worth  4%,  what  did  he  gain? 

4.  A  savings  bank  account  was  opened  July  1,  1914,  with  a 
deposit  of  f  800.  Interest  was  credited  every  6  mo.  at  4%. 
No  withdrawals  or  subsequent  deposits  having  been  made,  what 
was  the  balance  of  the  account  Jan.  1,  1920  ? 


INTEREST  325 

5.  The  note  on  page  314  was  not  paid  until  May  27.  How 
much  was  due  the  holder  of  the  note  on  that  date  ? 

6.  Jan.  1, 1915,  B  invested  $24,000  in  a  manufacturing  busi- 
ness. July  1,  1917,  he  withdrew  $33,000,  which  sum  included 
the  original  investment  and  the  net  gains.  What  average 
yearly  per  cent  of  simple  interest  did  the  investment  yield  ? 

7.  Derby  &  Co.  offer  B  the  following  terms:  Yjq,  Vso*  '^^^'  ^"^ 
B  bought  a  bill  of  goods  amounting  to  $4000  which  he  paid  Jan. 
31.  What  rate  of  interest  did  he  practically  pay  on  the  net 
amount  of  the  bill  by  not  taking  advantage  of  the  cash  offer  ? 

8.  In  a  certain  town  the  taxes  are  due  Sept.  15  of  each  year, 
and  all  taxes  unpaid  by  Oct.  15  are  subject  to  interest  from  the 
date  they  are  due,  at  6%.  The  following  taxes  were  paid  on 
the  dates  named:  Oct.  18,  $68.40;  Oct.  21,  $22.50;  Oct.  25, 
$132.75  ;  Oct.  31,  $98  ;  Nov.  11,  $176.80  ;  Nov.  23,  $326.30; 
Dec.  2,  $45  ;  Dec.  16,  $13.25  ;  Dec.  29,  $21.  How  much  in- 
terest was  paid,  the  time  being  the  exact  number  of  days  ? 

9.  Jan.  1,  1915,  F  bought  a  piece  of  city  property  for 
$20,000,  paid  cash  $4000,  and  gave  a  note  and  mortgage  for 
5  yr.  without  interest,  to  secure  the  balance.  To  cover  the  in- 
terest, which  it  was  agreed  should  be  met  quarterly,  he  gave 
twenty  notes  for  $240  each,  one  maturing  every  three  months. 
The  first  five  installments  of  interest  were  paid  when  due,  and  the 
balance  of  the  mortgage  and  the  interest  were  paid  Jan.  1, 1920. 
Find  the  final  payment. 


CHAPTER   XXVI 

BANK  DISCOUNT 
ORAL  EXERCISE 

1.  What  is  meant  by  a  promissory  note  ?  by  the  face  of  a 
note  ?  by  the  time  ?  by  the  maker  ?  by  the  payee  ? 

2.  How  would  you  word  a  promissory  note  for  $600,  dated 
at  your  place  to-day,  payable  in  60  da.  at  a  bank  in  your  place, 
with  interest  at  5%,  to  C.  B.  Powell,  signed  by  yourself? 

3.  What  is  meant  by  negotiable?  by  indorsing  a  note? 
Illustrate  a  blank  indorsement ;  an  indorsement  in  full  ;  a 
qualified  indorsement. 

404.  A  commercial  bank  is  an  institution  chartered  by  law  to 
receive  and  loan  money,  to  facilitate  the  transmission  of  money 
and  the  collection  of  negotiable  paper,  and,  in  some  cases,  to 
furnish  a  circulating  medium. 

405.  If  the  holder  (owner)  of  a  promissory  note  wishes  to 
use  the  money  promised  before  it  becomes  due,  a  commercial 
bank  will  usually  buy  th«  note,  provided  the  holder  can  show 
that  it  will  be  paid  at  maturity,  that  is,  when  it  becomes  due. 
This  is  called  discounting  the  note. 


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BANK  DISCOUNT  327 

406.  A  commercial  draft  is  now  frequently  used,  instead  of 
tlie  promissory  note,  as  security  for  the  payment  of  goods  sold 
on  credit.  Such  a  draft  may  be  defined  as  a  written  order  in 
which  one  person  directs  another  to  pay  a  specified  sum  of 
money  to  the  order  of  himself  or  to  a  third  person. 

The  circumstances  under  which  the  foregoing  draft  was  drawn  are  as 
follows :  Geo.  H.  Catchpole  sold  Frank  G.  Hill  goods  amounting  to  $460.80. 
Terms :  30-da.  draft.  The  draft  and  an  invoice  were  made  out  and  sent 
to  Frank  G.  Hill  by  mail.  Frank  G.  Hill  accepted  the  draft,  that  is,  signi- 
fied his  intention  to  pay  it  by  writing  the  word  accepted,  the  date,  and  his 
name  across  the  face.  The  draft  was  then  returned  to  Geo.  H.  Catchpole, 
who  may  discount  it  the  same  as  he  would  an  ordinary  promissory  note. 

The  parties  to  a  draft  are  the  drawer,  the  drawee,  and  the  payee.  In  the 
foregoing  draft,  George  H.  Catchpole  is  both  the  drawer  and  the  payee, 
and  Frank  G.  Hill  is  the  drawee. 

A  draft  payable  after  sight  begins  to  mature  from  the  date  on 'which  it  is 
accepted.  An  acceptance  must,  therefore,  be  dated  in  a  draft  payable  after 
sight,  but  it  may  or  may  not  be  dated  in  a  draft  payable  after  date. 


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Some  states  allow  three  days  of  grace  for  the  payment  of  notes  and  other 
negotiable  paper.  Days  of  grace  are  obsolete  in  so  many  of  the  states  that 
they  are  not  considered  in  the  exercises  in  this  book.  Some  states  provide 
that  when  paper  matures  on  Sunday  or  a  legal  holiday  it  must  be  paid  the 
day  preceding  such  Sunday  or  legal  holiday ;  others  provide  that  it  must  be 
paid  on  the  day  following.  To  hold  all  interested  parties,  the  laws  of  any 
given  state  should  always  be  observed.  When  the  time  of  negotiable  paper 
is  expressed  in  months,  calendar  months  are  used  to  determine  the  date  of 
maturity ;  but  when  the  time  is  expressed  in  days,  the  exact  number  of  days 
is  used.  Thus,  a  note  payable  2  mo.  after  July  15  is  due  Sept.  15 ;  but  a 
note  payable  60  da.  after  July  15  is  due  Sept.  13.  Paper  payable  1  mo. 
from  May  31,  Aug.  31,  etc.,  is  due  June  30,  Sept.  30,  etc. 


328 


PEACTICAL  BUSINESS  ARITHMETIC 


Maturity  Table 


407.  The  time  from  the  date  of  discount  to  the  maturity  of 
paper  is  called  the  term  of  discount ;  the  whole  sum  specified  to 
be  paid  at  maturity,  the  value,  or  amount,  of  the  paper. 

The  term  of  discount  is  usually  the  exact  number  of  days  from  the  date  of 
discount  to  the  date  of  maturity.  Some  banks,  however,  find  the  term  of 
discount  by  compound  subtraction,  and  then  reduce  the  time  to  days ;  e.g. 
the  term  of  discount  on  a  note  due  May  6  and  discounted  Mar.  1  is  counted 
as  2  mo.  5  da.,  or  65  da.  In  this  text  the  term  of  discount  is  the  exact  number 
of  days  from  the  date  of  discount  to  the  maturity  of  the  paper. 

408.  The  reduction  made  by  a  bank  for  advancing  money  on 
negotiable  paper  not  due  is  called  bank 
discount.     The  value  of  negotiable  paper 
at  maturity,  minus  the  bank  discount,  is 
called  the  proceeds. 

Bank  discount  is  always  the  simple  interest  for 
the  term  of  discount  on  the  whole  sum  specified  to 
be  paid  at  maturity. 

409.  The  accompanying  maturity  table 
is  sometimes  used  by  bankers  in  finding 
the  maturity  of  notes  and  drafts.  The 
following  examples  illustrate  its  use. 

410.  Examples,   l.    Find   the    maturity 

of  a  note  payable  (a)  6  mo.  from  Apr.  27, 

1915;   (6)  6  mo.  from  Sept.  25,  1915. 

Solutions,  (a)  Referring  to  the  table,  observe 
that  April  is  the  4th  month;  adding  4  and  6,  the 
result  is  10,  and  the  10th  month  (see  number  on  left) 
is  October.     The  note  is  therefore  due  Oct.  27,  1915. 

(&)  September  is  the  9th  month.  9  +  6  =  15,  and  the  15th  month  (see  number 
on  right)  is  March  of  the  next  year.     The  note  is  therefore  due  Mar.  25,  1916. 

2.    Find  the  maturity  of  a  note  payable  90  da.  from  Jan.  18, 

1916. 

Solution.  1  +  3  =  4,  and  the  4th  month  is  April.  If  the  note  were  pay- 
able in  3  mo.,  it  would  be  due  Apr.  18.  Keferring  to  the  table,  note  that  2 
da.  (1  da.  +  1  da.)  must  be  subtracted  for  January  and  March,  and  2  da.  added 
for  February.     The  note  is  therefore  due  Apr.  18. 

After  the  student  has  become  familiar  with  the  principles  of  the  table  it  will 
not  be  found  necessary  to  consult  it. 


1 

Jan.  -  1   13 

2 

Feb.  +  2 

14 

3 

Mar.  -  1 

15 
16 

4 

Apr. 

5 
6 

May-  1 

17 

June 

18 

7 

July  -  1 

19 

8 

Aug.  -  1 

20 
21 

9 

Sept. 

10 

Oct.  -  1 

22 

11 

Nov. 

23 
24 

12 

Dec.  -  1 

BANK   DISCOUNT 


329 


ORAL 

EXERCISE 

Find  the  maturity  of  each  of  the  following  notes  : 

Date 

Time 

Date 

Time 

1.    Apr.  6,  1915 

30  da. 

6.    Jan.  30,  1916 

30  da. 

2.    Oct.  6,  1916 

3  mo. 

7.    Jan.  31,  1915 

30  da. 

3.    Nov.  9,  1915 

60  da. 

8.    May  10,  1916 

90  da. 

4.    Jan.  31,  1916 

1  mo. 

9.    June  19,  1916 

60  da. 

5.    Sept.  18,  1915 

.       90  da. 

10.   Nov.  15,  1916 

30  da. 

Fi7id  the  maturity  of  each  of  the  follotving  acceptances : 

J.                     Time  after 
"^^^                     Date 

Datk 

Time  after 
Date 

11.    Apr.  3 

30  da. 

14.    Dec.  31 

2  mo. 

12.    May  5 

60  da. 

15.    Jan.  12 

1  mo. 

13.    Jan.  29 

1  mo. 

16.    Feb.  18 

3  mo. 

Find  the  maturity  of  each  of  the  following  acceptances  : 

Date              Time  after 

Date 

riME  after 

Accepted 

Sight 

Accepted 

Sight 

17.    Aug.  12 

3  mo. 

20.    Apr.  25 

60  da. 

18.    Sept.  18 

2  mo. 

21.    May  17 

3  mo. 

19.    Oct.   30       . 

4  mo. 

22.    June  18 

30  da. 

WRITTEN    EXERCISE 

Find  the  maturity  and  the  term  of  discount 


Date 

Time 

Discounted 

1.    Jan.   16, 

1916 

3  mo. 

Mar.  1 

2.    Jan.   31, 

1916 

1  mo. 

Feb.  3 

3.    Feb.  12, 

1916 

90  da. 

Mar.  2 

4.  •  Feb.  24, 

1916 

60  da. 

Apr.  1 

5.    Mar.  31, 

1916 

90  da. 

May  13 

Date  of  Draft 

Time  after  Date 

Date  Accepted 

Date  Discounted 

6.    Feb.  7 

60  da. 

Feb.    8 

Feb.    9 

7.    Mar.  12 

30  da. 

Mar.   12 

Mar.   15 

Date  of  Draft 

Time  after  Sight 

Date  Accepted 

Date  Discounted 

8.    May  31 

60  da. 

May  31 

June  3 

9.    Mar.  17 

90  da. 

Mar.  20 

Mar.  21 

330 


PRACTICAL   BUSINESS   ARITHMETIC 


411.    The  following  time  table  is  frequently  used  by  bankers 
in  finding  the  exact  number  of  days  between  any  two  dates : 

Table  of  Time 


From  Any 

Dai 

To  THE  Same  Day  of  the  Next 

OF 

Jan. 

Feb. 

Mar. 
59 

Apr. 
90 

May 
120 

June 
151 

July 
181 

Aug. 
212 

Sept. 
243 

Oct. 
273 

Nov. 
304 

Dec. 

January  .... 

365 

31 

334 

February  . 

334 

365 

28 

59 

89 

120 

150 

181 

212 

242 

273 

303 

March 

306 

337 

365 

31 

61 

92 

122 

153 

184 

214 

245 

275 

April  .  . 

275 

306 

334 

365 

30 

61 

91 

122 

153 

183 

214 

244 

May  .  .  - 

245 

276 

304 

335 

365 

31 

61 

92 

123 

153 

184 

214 

June  .  .  . 

214 

245 

273 

304 

334 

365 

30 

61 

92 

122 

153 

183 

July  .  . 

184 

215 

243 

274 

304 

335 

365 

31 

62 

92 

123 

153 

August  .' 

153 

184 

212 

243 

273 

304 

334 

365 

31 

61 

92 

122 

September 

122 

153 

181 

212 

242 

273 

303 

334 

365 

30 

61 

91 

October  . 

92 

123 

151 

182 

212 

243 

273 

304 

335 

365 

31 

61 

November 

61 

92 

120 

151 

181 

212 

242 

273 

304 

334 

365 

30 

December 

31 

62 

90 

121 

151 

182 

212 

243 

274 

304 

335 

365 

The  exact  number  of  days  from  any  day  of  any  month  to  the  correspond- 
ing day  of  any  other  month,  within  a  year,  is  found  in  the  column  of  the 
last  month  directly  opposite  the  line  of  the  first  month.  Thus,  from  June 
6  to  Sept.  6  is  92  da. ;  from  Apr.  1  to  Oct.  1  is  183  da. ;  from  Aug.  26  to 
Dec.  26  is  122  da.  The  exact  number  of  days  between  any  two  dates,  leap 
years  excepted,  is  found  as  in  the  following  illustrations : 

412.    Examples,    i.    How  many  days  from  Mar.  1  to  May  11? 

Solution.  From  Mar.  1  to  May  1  is  61  da.  From  May  1  to  May  11  is  10 
da.     61  da.  +  10  da.  =  71  da.,  the  required  result. 

2.    How  many  days  from  July  26  to  Oct.  6  ? 

Solution.  From  July  26  to  Oct.  26  is  92  da.  From  Oct.  26  back  to  Oct.  6 
is  20  da.     92  da.  —  20  da.  =  72  da.,  the  required  result. 

ORAL  EXERCISE 

By  the  table  find  the  exact  number  of  day%  from : 

1.  July  8  to  Sept.  8.  7. 

2.  Jan.  6  to  Mar.  6.  8. 

3.  Jan.  23  to  June  23.  9. 

4.  Feb.  13  to  July  13.  lo. 

5.  Mar.  11  to  Sept.  11.  ii. 


6.    Mar.  21  to  Aug.  21. 


12. 


May  31  to  Aug.  1. 
Feb.  23  to  Sept.  23. 
Mar.  24  to  July  12. 
May  11  to  Aug.  31. 
Aug.  15  to  Dec.  10. 
Nov.  25  to  Mar.  25. 


BANK   DISCOUNT 


331 


413.  Examples,  l.  Find  the  proceeds  of  a  note  for  13000, 
payable  in  78  da.,  discounted  at  6%. 

Solution.     78  da.  =  the  term  of  discount. 
$39  =  the  bank  discount. 
$3000  —  $39  =  $2961,  the  proceeds. 

2.  A  note  for  16000  payable  in  60  da.  from  May  10,  1915, 
with  interest  at  6%,  is  discounted  May  25,  at  6%.  Find  the 
maturity,  the  term  of  discount,  the  bank  discount,  and  the 
proceeds. 

Solution.     July  9,  1915  =  the  maturity. 

45  da.  =  the  term  of  discount. 

$  60  =  the  interest  on  the  note  for  60  da. 
$6060  =  the  value  of  the  note  at  maturity. 
$45.45  =  the  bank  discount. 
$6014.55  =  the  proceeds. 

414.  The  accompanying  diagram  illustrates  a  convenient 
outline  for  learning  the  proper 
method  of  computing  bank  dis- 
count. It  will  be  observed  that 
the  first  problem  is  an  interest- 
bearing  note,  and  the  second 
problem  a  non-interest-bearing 
note.  The  items  in  black  ink 
are  taken  from  the  problem,  and 
the  items  in  red  ink  are  found 
as  previously  explained. 

WRITTEN  EXERCISE 

1.  Assuming  that  the  model  note,  page  9,  was  discounted 
July  2,  at  6%,  find  the  bank  discount  and  the  proceeds. 

2.  Assuming  that  the  model  note,  page  314,  was  discounted 
Jan.  20,  at  6%,  find  the  bank  discount  and  the  proceeds. 

3.  Assuming  that  the  model  note,  page  316,  was  discounted 
Aug.  26,  at  6  %,  find  the  bank  discount  and  the  proceeds. 

4.  Assuming  that  the  model  draft,  page  326,  was  discounted 
May  15,  at  6  % ,  find  the  bank  discount  and  the  proceeds. 


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332  PRACTICAL   BUSINESS   ARITHMETIC 

5.  Assuming  that  the  model  draft,  page  327,  was  discounted 
April  12,  at  6%,  find  the  bank  discount  and  the  proceeds. 

6.  Find  the  proceeds  of  the  following  joint  note: 
$895.40  Baltimore,  Md.,  May  25,  1915. 

Six  months  after  date,  for  value  received,  we  promise  to  pay 
to  the  order  of  Ralph  D.  Gibson  Eight  Hundred  Ninety-five 
jYq  Dollars,  at  Exchange  National  Bank. 

Seth  M.  Bullard. 
Discounted  July  2,  1915,  at  5%.  Isaac  C.  Watkins. 

7.  Find  the  proceeds  of  the  following  joint  and  several  note: 
$1000.00  Columbus,  O.,  May  1,  1915. 

Three  months  after  date  we  jointly  and  severally  promise  to 
pay  to  the  order  of  Wilson  N.  Burton  One  Thousand  Dollars, 
at  Second  National  Bank,  Columbus,  O.,  with  interest  at  6%. 

Value  received.  John  M.  Sellers. 

Discounted  June  2,  1915,  at  6  %.         Daniel  W.  Sheldon. 

8.  Find  the  proceeds  of  the  following  firm  note: 
$1250.00  St.  Louis,  Mo.,  Aug.  20,  1915. 

Ninety  days  after  date  we  promise  to  pay  to  the  order  of 
C.  M.  Courtwright  Twelve  Hundred  Fifty  Dollars,  at  the 
National  Bank  of  Redemption,  with  interest  at  5  % . 

Value  received.  J.  M.  Cox  &  Son. 

Discounted  Sept.  1, 1915,  at  6  %. 

9.  Sept.  26  you  sold  R.  M.  Stein,  Portland,  Me.,  a  bill  of 
hardware  amounting  to  $2480,  less  20  %,  25  %,  and  10  %.  Terms: 
J  by  60-da.  note  with  interest  at  6  %  ;  J-  on  account  60  da.  What 
was  the  amount  of  the  note  which  was  this  day  received  ? 

10.  Oct.  12  you  discounted  at  Union  Bank,  at  6%,  R.  M. 
Stein's  note  received  Sept.  26,  the  bank  giving  you  credit  for 
the  proceeds.  If  the  bank  charges  -^q  %  for  collecting  out-of- 
town  paper,  what  was  the  amount  of  the  proceeds  credited  ? 

A  small  fee  called  collection  and  exchange  is  sometimes  charged  on 
discounted  paper  payable  out  of  town.  The  charge  is  by  no  means 
uniform,  being  controlled  largely  by  the  size  of  the  depositor's  account  and 
the  general  custom  of  the  banks  in  any  given  locality. 


BANK  DISCOUNT 


333 


11.  The  following  is  a  part  of  a  page  from  a  bank's  discount 
register.  Copy  it,  supplying  all  missing  terms.  The  notes 
were  all  discounted  June  17. 


No. 

Date  of 

Time 

When 

Term  op 

Rate  of 

Value  of 

Disc. 

Coll.  & 

Proceeds 

Papkr 
Apr.  25 

Due 

Discount 

Discount 

Paper 

EXCH. 

Credited 

20 

3  mo. 

6% 

2000 

00 

21 

May  1 

3  mo. 

6% 

3500 

00 

3 

50 

22 

Apr.  1 

90  da. 

6% 

1500 

00 

23 

Apr.  15 

90  da. 

6% 

900 

60 

24 

June  15 

30  da. 

6% 

378 

90 

38 

12.  Sept.  15  your  balance  m  the  First  National  Bank  was 
S  1725.90.  You  immediately  offered  for  discount,  at  6%,  the  fol- 
lowing notes,  the  proceeds  of  which  were  to  be  placed  to  your 
credit :  E.  M.  Robinson's  30-day  note  dated  Sept.  1,  for  S  300 ; 
C.  E.  Reardon's  note  payable  3  mo.  from  July  25,  with  interest 
at  6%,  for  $427.65;  C.  W.  Allen's  60-day  note  dated  Aug.  1, 
for  S  321.17;  F.  H.  Clark's  60-day  note  dated  July  30,  for 
S1500.  What  was  your  credit  at  the  bank  after  discounting  the 
notes  ? 

13.  April  6,  1915,  Peter  W.  Berger  has  on  deposit  in  the 
First  National  Bank  $523.87.  He  draws  a  check  for  11176.45, 
and  then  discounts  the  following  notes  at  the  bank,  at  6%, 
receiving  credit  for  the  proceeds.  What  was  the  balance  of  his 
account  after  the  notes  were  discounted  and  credited  ? 


1 346. 50  Hartford,  Conn.,  Mar.  1, 1915. 

Ninety  days  after  date  I  promise  to  pay  Peter  W.  Ber- 
ger, or  order,  Three  Hundred  Forty-six  -f^^  Dollars,  at  First 
National  Bank,  Hartford,  Conn. 

Value  received.  Henry  S.  Lane. 

b. 
1575.00  Hartford,  Conn.,  Feb.  1, 1915. 

Aug.  1,  1915,  I  promise  to  pay  Peter  W.  Berger,  or  order, 
Five  Hundred  Seventy -five  Dollars,  at  Second  National  Bank, 
Hartford,  Conn. 

Value  received.  Samuel  D.  Skiff. 


334 


PRACTICAL   BUSINESS    ARITHMETIC 


14.  July  18,  C.  B.  Snow's  bank  balance  is  1312.90.  He  dis- 
counts at  6  %  the  following  drafts,  and  then  issues  a  check  in 
payment  for  5  sewing  machines  at  175,  less  20%  and  25%. 
What  is  the  amount  of  his  balance  after  issuing  the  check? 


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BANK  LOANS 

415.  The  foregoing  exercises  have  reference  to  paper  bought 
or  discounted  by  a  bank.  Money  is  frequently  loaned  upon 
the  notes  of  the  borrower,  indorsed  by  some  one  of  known 
financial  ability,  or  secured  by  the  deposit  of  stocks,  bonds, 
warehouse  receipts,  or  other  collaterals.  These  notes,  if  drawn 
on  time,  are  not  interest-bearing,  but  the  bank  discounts  them 
by  deducting  from  their  face  the  interest  for  the  full  time. 


BANK   DISCOUNT  335 

416.  Loans  are  sometimes  made  on  call  or  demand  notes  ;  that 
is,  on  notes  that  can  be  called  or  demanded  at  any  time  after 
they  are  made.  These  notes  are  interest-bearing  and  are  drawn 
for  the  exact  sum  loaned. 

Call  or  demand  loans  generally  bear  a  lower  rate  of  interest  than  loans  on 
time.  They  are  made  principally  to  brokers  and  investors,  who  use  them 
to  pay  for  stocks ;  but  they  are  also  made  to  merchants  and  others  to  some 
extent.  Business  men,  however,  generally  prefer  to  borrow  on  time,  for 
they  do  not  wish  to  be  embarrassed  by  having  the  loans  called  in  at  an 
unexpected  time.  Time  loans  are  usually  drawn  for  thirty,  sixty,  or  ninety 
days.  If  the  borrower  requires  money  for  a  longer  period,  the  bank  will 
usually  allow  him  to  renew  the  note  when  it  falls  due. 

WRITTEN  EXERCISE 

1.  Jan.  7, 1915,  E.  L.  Jennings  &  Co.  desire  to  extend  their 
business,  and  for  this  purpose  borrow  money  at  6  %  of  the  First 
National  Bank  of  New  York,  on  the  following  note.  How 
much  will  the  bank  place  to  the  credit  of  E.  L.  Jennings  &  Co.  ? 

f.r<?(P(?^  JTew  York, Jl?^^^.  /, 19 

■ '  ~  '   ~  "  /^L^.-^?^ ^,-Z^,''g^^i^^^^  ' nff^f  date  -U^T/ promise  to  jtay  to 

the  order  of  "x^^^r^^  /Y^r7^,^f7-7^.'r:7^~A^^'??Z^^^ 


at  ^-1L^J>^^^  --^-^..-ftJk^.^:^^^  -^^TT-y^  .^y  ■ -  -  •  — 

Ytiiue  reeeioed 

2.  You  gave  the  Union  National  Bank,  of  your  city,  your 
note,  for  $1200,  at  60  da.,  indorsed  by  Williams  &  Rogers. 
How  much  cash  will  the  bank  advance  you,  if  discount  is 
deducted  at  the  rate  of  6%  ? 

3.  Howe  &  Rogers,  Buffalo,  N.Y.,  borrowed  il2,000  of  Mer- 
chants National  Bank  on  their  demand  note  secured  by  300 
shares  of  Missouri  Pacific  Railway  stock,  at  §50.  If  the  rate 
of  interest  was  2|  %,  how  much  was  required  for  settlement 
39  da.  after  the  loan  was  made  ? 


336  PRACTICAL   BUSINESS  ARITHMETIC 

4.  Jan.  2,  1915,  C.  W.  Allen  &  Co.,  brokers,  borrowed  of 
First  National  Bank,  Boston,  Mass.,  $15,000  on  the  following 
collateral  note.  How  much  was  required  for  full  settlement 
of  the  loan  57  da.  after  it  was  made  ? 


$Zj>^j2j2J:rrr^  Boston.  Mass., (fr7^<y^.   Z^ /  9 

(  y^'l^^iCt^^^^^'^.^i^.^^T^^^         fnr  value  rerekteil,  -J^/'Z—  prnmhe  to  pay  to  the  order  of 
r-:Zjyf^A-^/f^..i^'!^;^^  at  their  banking  house 

-T^J^^^.^^^r^^^4^^..<^^g^^^^  ^^  ^- ■  Hnllnrx 

As  collateral  security  for  the  payment  of  the  note  and  all  other  liabilities  to  said  bank,  either  absolute  or 
contingent,  now  existing  or  to  be  hereafter  incurred,  -<4/X~-  have  deposited  with  it : 

Should  the  market  value  of  the  same  decline,  ~Cc^~t—  promise  to  furnish  satisfactory  additional  collateral  on 
demand,  which  may  be  made  by  a  notice  in  writing,  sent  by  mail  or  otherwise,  to  ^:'-?o^*^ residence  or  place  of 
business.  On  the  nonperformance  of  either  of  the  above  promises  -U/-C-  authorize  the  holder  or  holders 
hereof  to  sell  said  collateral  and  any  collaterals  added  to  or  substituted  for  the  same,  without  notice,  at  public  or 
private  sale,  and  at  or  before  the  maturity  hereof,  he  or  they  giving  -*<-<^  credit  for  any  balance  of  the  net 
proceeds  of  such  sale  remaining  after  paying  all  sums  absolutely  or  contingently  due  and  then  or  thereafter 
payable  from  -'d-d-  to  said  holder  or  holders.  And  -'ttn-  authorize  said  holder  or  holders,  or  any  person  ia 
his  or  their  behalf,  to  purchase  at  any  such  sale. 


^^}'^^. 


0;^^^^M^-P.<;^ 


FINDING   THE   FACE 

417.  Example.  I  wish  to  borrow  $1980  of  a  bank.  For 
what  sum  must  I  issue  a  60-da.  note  to  obtain  the  amount,  dis- 
count being  at  the  rate  of  6%  ? 

Solution,  Let  the  face  of  the  note  =  1 1 

Then  the  bank  discount  =  $0.01 
And  the  proceeds  =  $0.99 

But  the  proceeds  =$1980 

$1980 -^  $0.99  =     2000 

.•.  the  face  of  the  note  is  2000  x  $1,  or  $2000. 

WRITTEN  EXERCISE 

1.  What  must  be  the  face  of  a  30-da.  note  in  order  that  when 
discounted  at  6  %  the  proceeds  will  be  %  1990  ?  Of  a  60-da.  note, 
same  conditions  ? 

2.  You  wish  to  borrow  f  3940  cash.  What  must  be  the  face 
of  a  90-da.  note  in  order  that  when  discounted  at  6  %  the  pro- 
ceeds will  be  the  required  sum? 


BANK  DISCOUNT 


337 


A  WRITTEN  REVIEW  TEST 

(Time,  approximately,  forty  minutes) 

Copy  each  of  the  following  problems ;  complete  the  work^  and 
check  the  result. 

AVhen  a  certain  number  of  days  is  written  in  the  Discount  column,  compute 
the  discount  at  67c  for  the  given  time.  When  jL%  is  written  in  the  Collection 
and  Exchange  column,  compute  the  collection  on  the  face  of  the  paper. 

When  copying  the  problem  do  not  copy  the  number  of  days  in  the  dis- 
count column,  nor  the  -^■^%  in  the  collection  and  exchange  column,  but  com- 
pute the  discount  or  the  collection  and  enter  the  result  in  the  required  column. 


Face  of  Paper 

Discount 

Coll.  &  Exch. 

Proceeds 

1.  $356.40 

$3.56 

$0.36 

? 

442.50 

2.21 

0.44 

? 

365.30 

60  da. 

0.37 

? 

297.45 

2.97 

tV% 

9 

175.40 

1.75 

0.18 

? 

217.50 

2.18 

iV% 

? 

246.30 

? 

30  da. 
? 

9 

? 

? 

Face  of  Paper 

Discount 

Coll.  &  Exch. 

Proceeds 

2.  S325.65 

$1.63 

$0.33 

? 

150.60 

90  da. 

0.15 

? 

327.85 

3.28 

0.33 

? 

180.96 

60  da. 

tV% 

? 

313.46 

3.13 

0.31 

? 

286.32 

1.43 

0.29 

? 

? 

? 

? 

? 

Face  of  Paper 

Discount 

Coll.  &  Exch. 

Proceeds 

3.  $422.50 

30  da. 

tV%     • 

? 

384.20 

$3.84 

$0.38 

? 

519.40 

5.19 

0.52 

? 

-  280.50 

90  da. 

0.28 

? 

375.90 
245.32 

1.25 
2.45 

9 

"    tV% 

• 
? 

? 

? 

? 

? 

CHAPTER   XXVII 

PARTIAL  PAYMENTS 
THE   UNITED   STATES   METHOD 

ORAL  EXERCISE 

1.  A  note  for  $500  bears  interest  at  6  %.  What  amount 
would  pay  the  note  and  interest  at  the  end  of  1  yr.  ? 

2.  Suppose  that  a  payment  of  f  130  was  made  at  the  end  of 
1  yr.  After  the  accrued  interest  has  been  paid,  how  much  is 
there  left  to  apply  to  the  face  of  the  note  ? 

3.  After  the  f  100  has  been  applied  to  the  face  of  the  note, 
what  amount  does  the  maker  continue  to  keep?  On  what  sum, 
therefore,  should  he  pay  interest  after  the  first  year  ? 

4.  The  maker  kept  the  remaining  $400  another  year.  How 
much  interest  was  then  due  ?     What  was  the  total  amount  due  ? 

5.  If  a  payment  of  $224  was  made  at  this  time,  what  amount 
still  remained  unpaid  ?  If  the  balance  of  the  note  was  paid 
three  years  after  it  was  issued,  what  was  the  amount  of  the 
payment  ? 

418.  Partial  payments  are  payments  in  part  of  a  note  or  bond. 

Such  payments  may  be  made  either  before  or  after  maturity.  They 
should  be  acknowledged  by  indorsement  on  the  back  of  a  note  or  bond. 
Current  forms  for  indorsing  partial  payments  on  notes  are  illustrated  on 
page  342. 

419.  The  United  States  method  of  partial  payments  (as  sug- 
gested in  problems  1-5  above)  has  been  adopted  by  the  Supreme 
Court  of  the  United  States,  and  made  the  legal  method  in  nearly 
all  the  states. 

This  is  the  method  ordinarily  used  by  individuals  when  the  time  between 
the  date  of  the  note  and  its  payment  is  more  than  one  year, 

338 


PARTIAL  PAYMENTS 


839 


420.  Example.  A  note  for  S1200,  dated  Jan.  1,  1915,  bear- 
ing interest  at  6%,  had  payments  indorsed  upon  it  as  follows: 
Mar.  1,  1915,  S212;  July  1,  1915,  $15;  Sept.  1,  1915,  S515; 
Nov.  1,  1915,  S175.  How  much  was  due  upon  the  note  at  final 
settlement,  Apr.  1,  1916. 

Solution 

Face  of  note $1200. 

Interest  from  Jan.  1,  1915,  to  Mar.  1,  1915  (2  mo.)  .         .         .  12. 

Amount  due  Mar.  1,  1915 

Payment  Mar.  1,  1915 

New  principal,  or  amount  to  draw  interest  after  Mar.  1,  1915 
Interest  from  Mar  1,  1915,  to  July  1,  1915  (4  mo.)  .         .         $20. 

Interest  exceeds  the  payment  and  the  principal  remains  unaltered. 
Interest  from  July  1,  1915,  to  Sept.  1,  1915  (2  mo.)  .         .         $10. 

Total  interest  due  Sept.  1, 1915 

Amount  due  Sept.  1,  1915 

Sum  of  the  payments  since  July  1  ($15  +  $515)      .... 
New  principal,  or  amount  to  draw  interest  after  Sept.l,  1915 
Interest  from  Sept.  1,  1915,  to  Nov.  1,  1915  (2  mo.) 

Amount  due  Nov.  1,  1915 

Payment  Nov.  1,  1915 

New  principal,  or  amount  to  draw  interest  after  Nov.  1, 1915 
Interest  from  Nov.  1,  1915,  to  Apr.  1,  1916  (5  mo.)         .         .         . 
Amount  due  at  settlement,  Apr.  1,  1916 


1212. 

212. 

1000. 


30. 
1030. 
530. 
500. 
5. 
505. 
175. 


330. 
8.25 


$338.25 

It  will  be  observed  in  the  foregoing  example  that  the  United  States  method 
provides :  (1)  that  the  payment  must  first  he  applied  to  discharge  the  accrued 
interest;  (2)  that  the  surplus,  if  any,  after  paying  the  interest  may  be  used  to 
diminish  the  principal ;  and  (3)  that  if  any  payment  is  less  than  the  accrued 
interest,  the  principal  remains  unaltered  until  some  payment  is  made  with  which 
the  preceding  neglected  payment  or  payments  is  more  than  sufficient  to  discharge 
the  accrued  interest. 

Condensed  Form   for  Written  "Work 


Dates 

Interest 
Periods 

Per  Cents 
OF  Interest 

Principals 

— 1 

Interests  on 
Principals 

Amounts  of 
Principals 

Payments 

Yr. 

Mo. 

Da. 

Yr. 

Mo. 

Da. 

1915 
1915 
1915 
1915 
1915 
1916 

1 

3 
7 
9 
11 
4 

2 
4 
2 
2 
5 

0 
0 
0 
0 
0 

$.01 
.02 
.01 
.01 
.025 

$1200.00 

1000.00 

1000.00 

500.00 

330.00 

$12.00 

20.00 

10.00 

5.00 

8.25 

$1212.00 

1030.00 
505.00 
338.25 

$212.00 

15.00 

515.00 

175.00 

1 

3 

0 

1 

3 

0 

$.075 

$338.25,  balance  due  Apr.  1,1916 

340  PRACTICAL   BUSINESS  ARITHMETIC 

When  there  are  many  payments,  the  work  may  be  simplified  as  shown  in 
the  foregoing  outline.  First  write  the  date  and  the  face  of  the  note  and  then 
the  dates  and  the  amounts  of  the  payments.  Next  find  the  interest  periods 
and  the  per  cents  of  interest.     Test  the  accuracy  of  the  work  to  this  point 

(1)  by  finding  the  difference  between  the  date  of  the  note  and  the  date 
of  settlement  and  comparing  it  with  the  sum  of  the  interest  periods ;  and 

(2)  by  comparing  the  sum  of  the  per  cents  of  interest  with  the  interest  on  $1 
for  the  full  time  as  shown  by  the  sum  of  the  interest  periods.  Complete 
the  remainder  of  the  work  as  suggested  by  the  outline. 

WRITTEN  EXERCISE 

-•^  1.  Jan.  2,  1916,  J.  E.  King  &  Co.  borrowed  of  E.  B. 
Peterson  &  Bro.  ^1000  and  gave  in  payment  a  note  payable  in 
6  mo.,  with  interest  at  5%.  July  2,  J.  E.  King  &  Co.  made  a 
payment  of  $500  and  issued  a  new  note  at  90  da.,  with  interest 
at  6  %  for  the  balance  due.     What  was  the  face  of  the  new  note? 

-f  2.  Jan.  30,  1915,  you  sold  Irwin  &  Co.  5  Eureka  Elevator 
Pumps  at  ^475,  less  a  trade  discount  of  16|%.  Terms:  note 
at  6  mo.  with  interest  at  6%.  What  was  the  amount  of  the 
note  ?  At  the  maturity  of  the  note  Irwin  &  Co.  paid  you  cash 
11000  and  gave  you  a  new  note  at  6  mb.,  with  interest  at  6% 
for  the  balance  due.  What  was  the  face  of  the  new  note? 
Sept.  1, 1915,  Irwin  &  Co.  paid  you  $200,  and  Dec.  1,  $300,  on 
their  note  of  July  30.  What  was  due  on  the  note  Feb.  9,  1916? 
^  3.  On  the  note  below  indorsements  were  made  as  follows: 
May  1,  1915,  $15;  Sept.  2,  1915,  $90;  Oct.  2,  1915,  $165; 
Jan.  2,  1916,  $125. 

$825.40  Omaha,  Neb.,  Jan.  2,  1915. 

Apr.  2,  1916,  I  promise  to  pay  Wilson  &  Allen,  or  order, 
Eight  Hundred  Twenty-five  -^q^-^  Dollars,  at  their  office,  with 
interest  at  6%. 

Value  received.  John  D.  Averill. 

What  was  due  at  the  maturity  of  the  note  ? 
4.    Find  the  amount  due  on  each  of  the  following  notes  July 
1,  1916  : 


PARTIAL   PAYMENTS  341 


a. 


'-^r^.J^^^..^^^  .^-^T^^-^^-f^^Ft^ ^ a^r  date  ^^^  promise  to  ptuf  to 

the  order  of  ^~lf4^^^ ^^^^^^J-'f^-J^  K^^?^^^^^ 


Value  received 


£^L^2^ 


^  Z-(P^r?.-^^—  ^Philadelphia,  ^a.,         J^^^^  /, /PZ^ 

""         ~    ^— '^<^Zr-.'-?7?^(<^^^7.,^?g7,'^^,<^^  '" ~      —promise  to  pay  to 

the  order  of  ^7^^Cr>/^W..-^^-gf^^^^fe         Z'^^^^^?^  ^ -  ■ 

Value  received 


C. 


^/2-(pr?<?-^^~-  SBoston.  ^^cc,       (^^^^  /. 791^^ 

Q^J^C^-rLCd-S'^j-fift.^-fT-n^i^^after  date,  for  value  received ^i:^i^promIae  to 

pauto^e  order  of~^^^7^^.^^  ^^^JxVx^-^^^g^S^V?^.-  K^^^^T 

^'^^^^/-^^^/^.^r^^.'fT-r^  >r-;h7.^yr^  ^^ S)ollars 

g^-:?%i^t-^-'^'<<???^^>^>^:^  ,  with  interest  at  the  rate  of^^::i:,^:2£^per  centum, 
per  annum  during  the  said=^A^Li3:2L^  and  for  such  further  time  as  the 
said  principal  sum  or  any  part  thereof  shall  remain  unpaid. 


342 


PEACTICAL   BUSINE!S8   AKITHMETIC 


\ 

^ 

^ 

^ 

^  ^ 

\ 

,^ 

■^  1 

.- 

^ 

i! 

PARTIAL   PAYMENTS  343 


THE  MERCHANTS'  METHOD 

ORAL   EXERCISE 

1.  A  note  for  f  500  is  dated  July  1,  1915,  payable  in  1  yr. 
with  interest  at  6%.  If  no  payments  have  been  made,  what  is 
due  on  the  note  July  1,  1916  ? 

2.  A  payment  of  1300  was  indorsed  on  the  note  Jan.  1,  1916. 
What  was  the  amount  of  this  payment  at  the  time  the  note  be- 
came due  ? 

3.  If  the  value  of  the  note  at  maturity  is  $530  and  the  value 
of  the  payment  $309,  what  is  the  balance  due  ? 

4.  By  the  United  States  method  what  is  the  balance  due  at 
maturity  on  the  note  described  in  problems  1  and  3  ?  How 
does  this  balance  compare  with  the  balance  in  problem  3  ? 

421.  The  merchants'  method  is  based  on  custom  rather  than 
on  legal  authority.  It  is  used  by  niost  banks  and  business  men 
on  short-time  notes  and  other  obligations. 

The  principles  of  the  merchants'  method  are  suggested  in  problems  1-3. 
This  method  provides  that :  (1)  the  face  of  the  note  shall  draw  interest  to  the 
date  of  settlement;  (2)  interest  shall  he  allowed  on  each  payment  from  the 
time  it  is  made  to  the  date  of  settlement. 

422.  Example.  On  a  note  for  $600,  dated  May  13,  1916,  pay- 
able on  demand,  with  interest  2A1  Qf^c,  payments  were  made  as 
follows:  June  28,  1916,  SlOO;  Aug.  28,  1916,  S200.  What 
was  due  at  settlement,  Sept.  28,  1916  ? 

Solution 

Face  of  note  May  13,  1916 $600.00 

Interest  from  May  13,  1916,  to  Sept.  28,  1916  (4  mo.  15  da.)     .         .  13.50 

Value  of  note  Sept.  28,  1916,  the  date  of  settlement  .         .         .       $613.50 

Payment  June  28,  1916 $100.00 

Interest  on  this  payment  from  June  28,  1916,  to  Sept.  28, 

1916  (3  mo.) 1.50 

Payment  Aug.  28,  1916 200.00 

Interest  on  this  payment  from  Aug.  28,  1916,  to  Sept.  28, 

1916  (1  mo.) 1.00 

Value  of  the  payments  Sept.  28,  1916,  the  date  of  settlement     .         .       $302.50 
Balance  due  Sept.  28,  1916,  the  date  of  settlement    ....      $311.00 


344 


PRACTICAL   BUSINESS  ARITHMETIC 


Some  houses  find  the  time  by  compound  subtraction  and  some  use  the 
exact  number  of  days.  In  the  following  exercise  find  the  difference  in  time 
by  compound  subtraction  in  problems  1-2,  and  use  the  exact  number  of  days 
in  problems  3-7. 

WRITTEN    EXERCISE 

1.  Solve  problem  a,  page  341,  by  the  merchants'  method  for 
partial  payments.     Compare  the  results  by  the  two  methods. 

2.  On  a  note  for  $1200,  dated  Apr.  16,  1916,  payable  on  de- 
mand, with  interest  at  4|  %,  payments  were  made  as  follows: 
June  15,  1916,  S500;  July  18,  1916,  $200.  What  was  due  at 
settlement,  Sept.  16,  1916  ? 

3.  June  15  you  borrowed  $  25,000  at  Traders'  National  Bank 
on  your  demand  note  secured  by  a  deposit  of  300  shares  of 
Illinois  Central  Railroad  Stock  at  $110.  June  27  you  paid 
$5000,  July  2,  $10,000,  and  July  30,  $5000.  Aug.  2  you 
paid  the  remainder  of  the  note  and  interest,  and  withdrew  the 
collaterals.  What  was  the  amount  of  the  last  payment,  money 
being  loaned  at  4i%? 

4.  The  following  is  a  partial  page  of  the  demand  and  loan 
register  of  a  large  bank.  Copy  it,  supplying  the  amount  of 
interest  due  Nov.  15,  money  being  loaned  at  4|  %. 


Charles  W.  Sherman 


No. 

Date 

LOANEL 

Amount 
>    Loaned 

Date  of 
Payment 

Part  of 
Loan 
Paid 

Balance 
of  Loan 

Inter- 
est 

Collateral 

Value  of 
Collat- 
eral 

347 

Apr.  1 

20,000 

00 

May 
July 
Sept. 
Nov. 

15 
1 
1 

15 

5,000 
5,000 
6,000 
4,000 

00 
00 
00 
00 

15,000 

10,000 

4,000 

00 
00 
00 

??? 
??? 
??? 
??? 
??? 

?? 
?? 
?? 
?? 
I? 

250  shares 
Peim.  R.R. 
Stock    .     . 

31,250 

00 

The  balance  due  by  the  merchants'  method  may  be  found  in  the  manner 
suggested  by  the  above  account.  The  interest  is  found  on  the  face  of  the 
note  to  the  date  of  the  first  payment.  The  payment  is  deducted  and  the  in- 
terest found  on  the  balance  to  the  date  of  the  second  payment,  and  so  on. 
The  results  obtained  by  this  process  are  exactly  the  same  as  the  results  ob- 
tained by  §  421. 


PARTIAL   PAYMENTS  345 

5.  Solve  problem  4  by  the  United  States  method  and  com- 
pare the  result  with  the  merchants'  method. 

6.  Assuming  that  the  collateral  note,  page  336,  has  the  fol- 
lowing payments  indorsed  on  its  back,  find  the  amount  due  at 
final  settlement,  Feb.  28,  1916.  Indorsements:  Jan.  15,  1916, 
$3000  ;  Jan.  31,  1916,  15000  ;  Feb.  5,  1916,  $1000. 

7.  A  collateral  note  dated  at  Philadelphia,  Pa.,  July  10, 1916, 
for  $20,000  payable  at  the  Quaker  City  National  Bank  is  in- 
dorsed as  follows  :  Aug.  8, 1916,  $3500  ;  Sept.  12, 1916,  $7500  ; 
Nov.  19,  1916,  $4000  ;  Dec.  31,  1916,  $5000.  What  was  due 
on  the  note  Dec.  31,  1916,  interest  being  at  the  rate  of  4%  ? 

To  solve  the  problem  copy  and  complete  the  following  interest  statement : 
./O  /) /)   rA      Philadelphia. <='^O^C-'^!>,    ^^ , 19 


To  THE  QUAKER  CITY  NATIONAL  BANK.  Dr. 

To  interest  on  demand  loans,  as  follows: 

^//^J-^^^fram      ^/^  tn       ^A 2.  rj ^  days,    $_ 


$    f  ^  (P O  ^Src^rx^      ^/a  tn      'V/g  __ZZ__days.    %_IJ^.LI_ 

$  J~^  ^  ^ -^  from    ■''/??  \cs    -VpP  ? />  flays,    $       ?F.?P 

Please  send  us  the  above  interest  on  or  Mnrp  ....^ti^?^^^^  /^.4^^^-yi..-L^^ 


>rASHIFR     I 


8.  Make  an  interest  statement,  similar  to  the   above,  for 
problem  6. 

9.  Make  an  interest  statement,  similar   to   the  above,  for 
problem  3. 

10.  Bring  to  the  class  a  canceled  note  on  which  partial  pay- 
ments are  recorded.  Find,  by  the  United  States  method  and  by 
the  merchants'  method,  the  amount  required  to  cancel  the  note. 
Which  method  is  the  better  for  the  debtor?  for  the  creditor? 


CHAPTER   XXVIII 


BANKERS'  DAILY  BALANCES 


423.  Some  commercial  banks  and  trust  companies  pay  inter- 
est on  the  daily  balances  of  their  depositors. 

Whether  interest  shall  be  allowed  on  a  depositor's  account  is  usually 
determined  by  the  size  of  his  daily  balances.  As  a  rule,  no  interest  is 
allowed  on  small  balances  subject  to  check.  All  balances  not  subject  to 
check  usually  draw  interest.  In  an  active  account,  that  is,  an  account  in  which 
the  balance  changes  frequently,  interest  is  seldom  allowed  except  on  an  even 
number  of  hundred  dollars,  and  all  parts  of  a  hundred  dollars  are  rejected. 

The  form  of  the  book  in  which  accounts  with  depositors  are  recorded 
varies  in  different  sections.  What  is  known  as  the  Boston  individual  ledger 
(see  form,  page  38)  is  extensively  used.  Another  form  of  depositors'  ledger 
is  that  shown  in  the  example  below. 

424.  Example.  Verify  the  balance  due  on  the  following  ac- 
count beginning  Mar.  1,  1916,  interest  settlements  being  made 
monthly  at  3%. 

M.  W.  Faknham 


Explanation 

Date 

F. 

Debit 

Balance 

Credit 

F. 

Date 

Explanation 

1916 

1056 

25 

1915-6 

Dec. 

31 

1650 

25 

600 

00 

15 

Jan. 

7 

Currency 

2556 

25 

900 

00 

15 

11 

N.  Y.  draft 

Check 

Jan. 

15 

14 

510 

00 

2046 

25 

3746 

25 

1700 

00 

17 

Jan. 

22 

N.  Y.  draft 

Note 

Jan. 

25 

16 

210 

00 

3536 

25 

Check 

28 

16 

500 

00 

3036 

25 

3042 

08 

5 

83 

17 

Jan. 

31 

Interest 

4042 

08 

1000 

00 

21 

Feb. 

8 

N.  Y.  draft 

Check 

Feb. 

15 

20 

500 

00 

3542 

08 

Check 

22 

22 

1340 

00 

2202 

08 

2209 

49 

7 

41 

23 

Feb. 

28 

Interest 

Solution.  The  credit  slip  on  page  347  shows  a  form  used  for  recording  the 
daily  balances.  Only  two  money  columns  are  used,  one  for  hundreds  and  the 
other  for  thousands.  No  interest  is  computed  except  on  an  even  number  of 
hundred  dollars,  and  all  parts  of  a  hundred  dollars  are  rejected. 

346 


BANKEKS'   DAILY   BALANCES 


347 


Beginning  Jan.  1  the  daily  balance  of  M.  W.  Farnham's  account  for 
6  da.  was  $1056.25;  record  $1000  on  the  credit  slip  as  shown  in  the  margin. 
A  deposit  of  $600  was  made  Jan.  7,  making  the  balance  $1656.25  for  the  next 
4  da.;  record  $1600  on  the  credit  slip  as  shown  in  the  margin.  A  deposit  of 
$  900  on  Jan.  1 1  made  the  balance  $  2556.25 
for  the  next  4  da.;  record  $2500  on  the 
credit  slip  as  shown  in  the  margin.  A  with- 
drawal of  $  510  on  Jan.  15  left  a  balance  of 
$2046.25  for  the  next  7  da.;  record  $2000 
on  the  credit  slip  as  shown  in  the  margin. 
A  deposit  of  $1700  on  Jan.  22  made  the 
balance  $3746.25  for  the  next  3  da.;  record 
$3700  on  the  credit  slip  as  shown  in  the  mar- 
gin. A  withdrawal  of  $210  on  Jan.  25  left 
a  balance  of  $3536.25  for  the  next  3  da.; 
record  $3500  on  the  credit  slip.  A  with- 
drawal of  $500  on  Jan.  28  left  a  balance  of 
$3036.25  for  the  next  4  da.  This  records 
the  balance  for  each  day  in  January.  Add- 
ing these  balances  the  result  is  $70,000,  and 
the  interest  on  this  sum  for  1  da.  at  3%  is 
$  5. 83.  Adding  $  5. 83  to  $  3036. 25  gives  the 
balance  to  the  credit  of  the  depositor  Feb.  1 
as  $3042.08. 

Enter  the  daily  balances  for  February  as 
shown  in  the  margin.  The  result  is  found 
to  be  $88,900,  and  the  interest  on  this  sum 
for  1  da.  at  3%  is  $7.41.  $7.41  added  to 
the  balance  of  the  depositor's  account  Feb. 
28  gives  $  2209.49  as  the  balance  to  his  credit 
beginning  Mar.  1. 

In  practice  the  daily  balances  are  usually 
written  as  shown  in  the  February  column 
of  the  accompanying  credit  slip.  The  total 
is  then  found  by  multiplication  and  addi- 
tion. Thus,  the  total  of  the  February  col- 
umnis7  x  §3000  +  7  x  $4U00  +  7  x  $3500 
-h  7  X  $2200,  or  $88,900. 

Some  accountants  also  use  the  pure 
interest  method  in  finding  the  amount  due. 
Thus,  the  interest  on  $3000  for  7  da.,  plus  the  interest  on  $4000  for  7  da.,  plus 
the  interest  on  $3500  for  7  da.,  plus  the  interest  on  $2200  for  7  da.  equals  $7.41, 
the  same  as  by  the  first  method. 

In  the  examples  which  follow  the  student  may  use  either  of  the  three  methods 
suggested. 


DAILY  CREDIT  BALANCES 
M.  W.  Farnham 

1007 

Jan. 

Feb. 

1 

2 

3 

4 

5 

6 

7 

8 

9 
10 
11 
12 
13 
14 
15 
16 
17 
18 
19 
20 
21 
22 
23 
24 
25 
26 
27 
28 
29 
30 
31 
Total 

1 
1 
1 
1 
1 
1 
1 
1 
1 
1 

2 
2 
2 
2 
2 
2 
2 
2 
2 
2 
2 
3 
3 
3 
3 
3 
3 

1 

3 
3 

6 
6 
6 
6 
5 
5 
5 
5 

T 
< 

7 
7 
5 
5 
5 

3 
4 

8 
2 

5 
2 

70 

0 

88 

9 
41 

Interest 

5 

83 

7 

348 


PKACTICAL   BUSINESS   ARITHMETIC 


WRITTEN  EXERCISE 

,  1.  The  Rochester  Trust  and  Safe  Deposit  Co.  allows  inter- 
est to  its  depositors  on  daily  balances  at  3  %  per  annum,  pay- 
able quarterly.  Find  the  cash  balance  of  the  following  account 
with  Chas.  M.  Sherman,  Apr.  1,  1916.  Jan.  1,  1916,  deposited 
11200;  Jan.  12  drew  out  1400;  Jan  30  deposited  1800; 
Jan.  31  drew  out  1400;  Feb.  10  deposited  1800;  Feb.  25 
drew  out  $100  ;  Mar.  10  deposited  1800  ;  Mar.  20  drew  out 
$900  ;  Mar.  25  deposited  |300. 

2.  At  the  close  of  an  interest  period,  Feb.  28,  1916,  Harvey 
&  Smith's  balance  with  the  Fidelity  Trust  Co.  was  $2246. 
During  the  month  of  March  they  made  the  following  deposits  : 
Mar.  3,  $2500;  Mar.  9,  11750;  Mar.  24,  12645.75;  Mar.  28, 
$1310.50  ;  Mar.  30,  $500.  They  also  drew  out  by  check  as  fol- 
lows: Mar.  4,  $1050;  Mar.  6,  $2000;  Mar.  8,  $720;  Mar.  12, 
$840.50;  Mar.  16,  $450;  Mar.  19,  $430;  Mar.  23,  $1000; 
Mar.  26,  $150;  Mar.  29,  $267.  How  much  interest  should  be 
credited  Mar.  31,  the  rate  being  3%  per  annum?  What  was 
the  balance  of  the  account  after  the  interest  was  credited? 

3.  Find  the  cash  balance  of  the  following  account  May  31, 
1916,  assuming  that  interest  is  allowed  on  daily  balances  at  3  % 
and  added  to  the  account  monthly. 


A. 

S.  OSBORN 

Explanation 

Date 

F. 

Debit 

Balance 

Credit 

F. 

Date 

Explanation 

1916 

1200 

00 

1916 

Feb. 

28 

Check 

Mar. 

12 

100 

00 

1500 
2000 

00 
00 

400 

500 

00 
00 

Mar. 

12 
25 

Currency 
Currency 

Check     . 

31 

100 

00 

2400 

** 

500 

* 

00 

31 
31 

N.  Y.  draft 
Interest 

**** 

** 

700 

00 

Apr. 

15 

N.  Y.  draft 

Note 

Apr. 

20 

50 

00 

**** 

** 

200 

00 

20 

N.  Y.  draft 

Check 

30 

1200 

00 

**** 

** 

* 

** 

30 

Interest 

**** 

** 

250 

00 

May 

10 

Currency 

Check 

May 

31 

500 

00 

**»* 

** 

* 

** 

31 

Interest 

CHAPTER   XXIX 

SAVINGS-BANK  ACCOUNTS 

425.  A  savings  bank  is  an  institution,  chartered  by  the  state, 
in  which  savings  or  earnings  are  deposited  and  put  to  interest. 

The  deposits  in  a  savings  bank  are  practically  payable  on  demand.  Most 
banks  reserve  the  right  to  require  notice  of  withdrawal  from  30  to  60  da. 
in  advance  ;  but  this  right  is  seldom  exercised. 

The  period  of  time  which  must  elapse  before  dividends  of  interest  are 
declared  is  called  the  interest  term.  Dividends  of  interest  are  usually  de- 
clared semiannually;  but  in  some  sections  they  are  declared  quarterly.  The 
stated  days  on  which  balances  begin  to  draw  interest  are  called  interest  days. 
In  some  savings  banks  deposits  begin  to  draw  interest  from  the  first  of  each 
quarter ;  in  others,  from  the  first  of  each  month. 

In  nearly  all  savings  banks,  only  such  sums  as  have  been  on  deposit  for 
the  full  time  between  the  interest  days  draw  interest.  Thus,  if  the  interest 
days  begin  on  the  first  of  each  quarter,  only  those  sums  that  have  been  on 
deposit  for  the  full  quarter  draw  interest. 

426.  Interest  is  computed  on  an  even  number  of  dollars, 
and  all  fractions  of  a  dollar  are  rejected.  When  interest  is  not 
withdrawn  it  is  placed  to  the  credit  of  the  depositor  and  draws 
interest  the  same  as  any  regular  deposit.  Savings  banks  there- 
fore allow  compound  interest. 

427.  Examples,  l.  In  the  Walker  Institution  for  Savings 
the  interest  term  is  6  mo.  and  the  interest  days  are  Jan.  1, 
Apr.  1,  July  1,  and  Oct.  1.  Verify  the  balance  due  on  the 
following  account  Jan.  1,  1916,  at  4  %. 

Solution.  The  account  was  opened  July  1,  1915,  by  a  deposit  of  $500. 
July  10  this  sum  was  increased  by  a  deposit  of  $10,  making  the  balance  $510; 
Aug.  14  this  sum  was  diminished  by  a  withdrawal  of  $  20,  making  the  balance 
$490;  Oct.  4  this  sum  was  diminished  by  a  withdrawal  of  $200,  making  the 
balance  $  290.  The  account  was  similarly  increased  and  diminished  until  Dec. 
31,  when  there  was  a  balance  of  $300.75  due  the  depositor. 

349 


350 


PRACTICAL  BUSINESS   AEITHMETIC 


*Jhe   nalken  institution  for  Savings 

in  account  with 

(                        \ 

DATE 

DEPOSITS 

INTEREST 

PAYMENTS 

BALANCE 

^/f/^ 

/ 

,ro  ^ 



v:f77/^ 

/^        / 

/  /? 

/  ^ 

_ 

.r/  ^ 

/^ 

2  ^ 

„ 

U£?  r; 

r^2 

^A 

Z/0  0 

_ 

7  ^ 

_ 

//7 

-7  0 

7^^ 

/ 
J  6/9 

'7S' 

^^^ 

/r 

A^^ 

A^/^  r> 

/ 

J/ 

/  lO  ^ 

.3  r7^ 

/ 

Q^^^y?^ 

/ 

y 

Jr'n 

>?  fJ  ^ 

^ 

The  smallest  balance  for  the  first  interest  period,  July  1  to  Oct.  1,  was  $490. 
The  interest  on  $490  for  3  mo.  at  4%  is  $4.90.  The  smallest  balance  for  the 
second  interest  period,  Oct.  1  to  Jan.  1,  was  $290.  The  interest  oh  $290  for 
3  mo.  at  4%  is  $2.90.  $4.90  plus  $2.90  equals  $7.80,  the  dividend  of  interest 
due  the  depositor  Jan.  1.  Since  this  sum  is  not  withdrawn,  it  is  placed  to  the 
credit  of  the  depositor,  making  his  balance  $308.55. 

2.  In  the  Warren  Institution  for  Savings  interest  dividends 
are  declared  semiannually  and  the  interest  days  are  Jan.  1, 
Apr.  1,  July  1,  and  Oct.  1.  Verify  the  balance  due  on  the 
following  account  Jan.  1,  1916,  at  4%. 


Cj)e  3S^an:m  institution  for  ^atainsa; 

^,         in  account  iiit^ 

/ 

DATE 

DEPOSITS 

INTEREST 

PAYMENTS 

BALANCE 

/ 

.^/^/7 

. 

.r/^^ 

. . 

4.. 

/ 

,3/0/9 

__ 

r^0 

_ 

jYt^^y 

//? 

/  /O  /O 

_ 

<^/y^ 



(L.2. 

/ 

/.t? 

, ^ 

^/,3 

, , 

'^fi:?^ 

/ 

/t 

?Y 

/ 

;^^ 

.j^M^n^, 

v 

SAVINGS-BANK  ACCOUNTS 


351 


Solution.  The  smallest  balance  for  the  first  interest  period  was  $500  ;  the 
interest  on  $  500  for  3  mo.  at  4  %  is  $  5.  The  smallest  balance  for  the  second 
interest  period  was  $800;  the  interest  on  $800  for  3  mo.  at  4%  is  $8, 
$ 5  +  $  8  =  $  13,  the  total  interest  due  the  depositor  July  1.  $900  +  $  13  =  $  913, 
This  balance  remained  unchanged  for  the  next  6  mo.  The  interest  on  $913  for 
6  mo.  at  4 %  is  $  18.26.  $  913  +  $  18.26  =  $  931.26,  the  amount  due  the  depositor 
Jan.  1,  1916. 

WRITTEN  EXERCISE 

1.  Solve  example  1  above,  assuming  that  the  interest  days 
are  the  first  day  of  each  month ;  also  example  2. 

2.  Copy  the  following  account,  supplying  the  missing 
amounts.  Interest  at  4|  %  ;  interest  days,  Jan.  1,  Apr.  1,  July  1, 
and  Oct.  1. 

MANHATTAN   SAVINGS  BANK 
In  Account  with  Mr.  Chas.  B.  Sherman 


Date 

Deposits 

Interest 

Payments 

Balance 

1915 

Jan. 

1 

600 

00 

*  *  * 

*  * 

Jan. 

31 

100 

00 

*  *  * 

*  * 

Mar. 

1 

250 

00 

*  *  * 

*  * 

May 

6 

50 

00 

*  *  * 

*   * 

May 

31 

100 

00 

*  *  * 

*  * 

July 

1 

*    * 

*  * 

*  *  * 

*   * 

3.    Copy  and  complete  the  following  account.      Interest  at 
4%  ;  interest  days,  Jan.  1,  Apr.  1,  July  1,  and  Oct.  1. 


FIDELITY  SAVINGS  BANK 
In  Account  with  Mr.  Frank  M.  Ellery 


Date 

Deposits 

Interest 

Payments 

Balance 

1915 

Jan. 

1 

300 

00 

*  *  * 

*    « 

Mar. 

6 

200 

00 

*  *  * 

*    * 

Mar. 

30 

125 

00 

*  *  * 

*    * 

Apr. 

17 

165 

50 

*  *  * 

*    * 

July 

1 

100 

00 

*   * 

*  * 

*    *    4^ 

*    * 

Aug. 

15 

75 

00 

*    *    * 

*    * 

Auff. 

31 

58 

40 

*    *    * 

*   * 

Oct. 

1 

250 

00 

*    *    * 

*    * 

Dec. 

1 

110 

50 

*    *    * 

*  Ma 

1916 

Jan. 

1 

*  * 

*  * 

*    *    * 

*  * 

352  PEAOTICAL   BUSINESS   AEITHMETIG 

POSTAL    SAVINGS   BANKS 

428.  The  law  establishing  postal  savings  banks  became  effec- 
tive in  the  United  States,  January  3,  1911.  Herewith  are  some 
of  the  leading  provisions  of  this  law. 

429.  An  account  may  be  opened  and  deposits  made  by  any 
person  of  the  age  of  10  yr.  or  over. 

430.  Deposits  will  be  accepted  only  from  individuals,  and  no 
account  will  be  opened  in  the  name  of  a  corporation,  associa- 
tion, society,  firm,  or  partnership,  or  in  the  name  of  two  or  more 
persons  jointly. 

431.  Deposits  may  be  accepted  without  regard  to  the  resi- 
dence of  the  depositor  or  the  post  office  of  which  he  is  a  patron, 
but  a  person  can  have  but  one  postal  savings  account,  either  at 
the  same  office  or  at  different  offices. 

432.  No  account  may  be  opened  for  less  than  SI,  nor  will 
fractions  of  a  dollar  be  accepted  for  deposit  at  any  time. 

433.  Postal  savings  deposits  will  be  evidenced  by  certificates 
in  fixed  denominations  of  $1,  S2,  S5,  $10,  S20,  $50,  issued  in 
the  name  of  the  depositor.  Such  certificates  are  non-transferable 
and  non-negotiable.  Each  certificate  must  bear  the  depositor's 
name,  the  number  of  his  account,  the  date  of  issue,  the  name 
of  the  office  receiving  the  deposit,  and  the  date  on  which  inter- 
est will  begin.  .Interest  will  begin  on  each  deposit  the  first  day 
of  the  month  following  the  deposit. 

A  deposit  on  March  1  will  not  begin  to  draw  interest  until  April  1. 

434.  Interest  at  the  rate  of  2%  per  annum  shall  be  allowed 
and  paid  on  the  amount  represented  by  each  postal  savings  cer- 
tificate for  each  full  year  that  it  remains  on  deposit.  No  interest 
will  be  allowed  for  a  fractional  portion  of  a  year.  Compound  in- 
terest is  not  allowed,  but  a  depositor  may  withdraw  interest  accrued 
and  make  a  new  deposit  of  it  which  will  then  draw  interest. 

435.  A  postal  savings  card  with  nine  postal  savings  stamps 
affixed  may  be  presented  and  accepted  as  a  deposit  for  $  1,  either 
in  opening  an  account  or  in  adding  to  an  existmg  account,  or  it 
may  be  redeemed  in  cash. 


SAVmGS-BANK   ACCOUNTS  353 

436.  Postal  savings  cards  and  stamps  are  transferable  and 
need  not  be  presented  for  deposit  by  the  original  purchaser. 
They  may  be  sold  to  any  person  in  any  quantity  desired. 

437.  A  depositor  may  surrender  his  deposits  in  whole  or  in 
part,  in  the  sum  of  S  20  or  any  multiple  thereof  up  to  $  500,  and 
receive  in  heu  of  such  surrendered  deposits  postal  savings  bonds 
in  appropriate  denominations.  Such  exchange  may  be  made  by 
a  depositor  as  of  January  1  and  July  1  of  each  year,  but  appli- 
cations therefor  shall  be  made  at  least  1  mo.  previously.  These 
bonds  bear  interest  at  the  rate  of  21  %  per  annum,  payable  semi- 
annually. 

WRITTEN    EXERCISE 

1.  If  John  A.  Sellman  deposited  S  7  on  the  tenth  day  of  each 
month  for  the  year  1911,  begmnmg  Jan.  10  and  making  his  last 
deposit  on  Dec.  10,  what  sum  would  be  to  his  credit  on  March  1, , 
1912?  on  Sept.  1,  1912? 

2.  If  John  A.  Gilson  deposited  $12  on  the  first  day  of  each 
alternate  month  for  the  year  1913,  begmning  Jan.  1,  what  sum 
would  be  to  his  credit  on  Jan.  1,  1914  ?  on  April  1,  1914  ? 

3.  If  no  additional  deposits  were  added  to  the  account  in 
problem  2,  what  sum  would  be  to  the  credit  of  Mr.  Gilson  on 
Jan.  1,1915? 

4.  Ralph  C.  Yarner  made  the  following  deposits  and  received 
postal  savings  certificates  therefor:  Nov.  4,  1911,  S15;  Mar. 
12,  1912,  $25;  July  11,  1912,  $30;  Oct.  2,  1912,  $23.  What 
was  due  on  this  account  July  1,  1915  ? 

5.  Henry  M.  Werner  made  the  following  deposits  and  received 
postal  savings  certificates  therefor:  Mar.  1,  1914,  $11;  June' 4, 
1914,  $19  ;  Sept.  8,  1914,  $10  ;  Dec.  23, 1914,  $10.  What  was 
due  on  this  account  Jan.  1,  1915  ?  on  Apr.  1,  1915  ? 


CHAPTER   XXX 

EXCHANGE 
DOMESTIC   EXCHANGE 

ORAL  EXERCISE 

1.  Mention  some  objections  to  sending  actual  money  by 
express. 

2.  If  $50  sent  by  mail  in  a  registered  letter  is  lost,  to  what 
extent  are  the  postal  authorities  liable  ? 

3.  In  what  ways  may  you  pay  a  debt  at  any  distant  point 
without  actually  sending  the  money  ? 

438.  The  process  of  settling  accounts  at  distant  points  with- 
out actually  sending  the  money  is  called  exchange. 

Money  Orders 

439.  Money  orders,  as  issued  by  post  offices,  express  com- 
panies, and  banks  are  frequently  used  in  making  payments 
at  a  distance. 

440.  A  postal  money  order  is  a  government  order  for  the 
payment  of  money,  issued  at  one  office  and  payable  at  another. 


6T59S^  Westfield,  Sta.l.Mass.  32^^ 

United  States  Postal  Money  Order 


RECEIVEO  PAYMENT: 

FACSIMILE.  OF  NO  VALUE 


Westfield,  Sta.1.  Mass.  3746^ 

J61596  ^Liy 

""  """""     Coupon  for  Payings  Office 


THIS  MONEY  ORDER  IS  NOT  OOOO 
•  FOR  MORE  THAN  LARGEST  AMOUNT 
■^  INDICATED  ON  LEFT-HAND  MAROiNl 
i     or  THE  ORDER  AND  / 


HON  OK  ERASURE! 


I  IT  VOID 


354 


EXCHANGE 


a55 


The  fees  (rate  of  exchange)  charged  for  postal  money  orders  are : 
For  orders  for  sums  not  exceeding 


12.50  3^ 

Over  2.50  to  $  5.00  hf 
Over  5.00  to  10.00  ^9 
Over  10.00  to  20.00  10^ 
Over  20.00  to    30.00  VI  f 


Over  $30.00  to  %  40.00  15;* 

Over     40.00  to       50.00  \^f 

Over     50.00  to       60.00  20;* 

Over     60.00  to       75.00  25;* 

Over     75.00  to     100.00  30;* 


The  maximum  amount  for  which  a  single  postal  money  order  may  be 
issued  is  $  100.  When  a  larger  sum  is  to  be  sent,  additional  orders  must  be 
obtained.  When  an  order  is  issued,  the  money  is  not  sent  from  one  post 
office  to  another.  The  transfer  is  merely  a  matter  of  bookkeeping,  the 
money  being  received  by  the  government  at  one  office  and  paid  out  at 
another.  If  a  postal  money  order  is  lost,  a  duplicate  may  be  obtained  from 
the  Post  Office  Department  at  Washington. 

441.  An  express  money  order  is  an  order  for  the  payment  of 
money,  issued  by  an  express  company  and  payable  at  any  of  its 
agencies. 


I 


When  Countersigned 

SrAOENTATPOINTOFtSSUe 


PaYTO  THE  ORDER  0F_^ 


EXPRESS  MONEY  ORDER 


The  Sum  of /.Lil^^;^^.^^..^'^^^ ju.?i 

VoT  GOOD  fOR  MORE  TMAH  THE  HIGHEST  PRllilTtB  HAg 


'"(^Tf^^S^^yt^^^J^ 


^lA^^^T^d^^iP^.--'?^'^.  .  .  State  orj^ 


The  fees  charged  for  express  money  orders  are  the  same  as  those  for  postal 
money  orders.  The  maximum  amount  for  which  a  single  express  money 
order  may  be  issued  is  $50.  A  postal  money  order  must  not  bear  more 
than  one  indorsement;  but  an  express  money  order  may  bear  any  number 
of  indorsements. 

442.  A  bank  money  order  (see  form,  page  356)  is  an  order 
for  the  payment  of  money  issued  by  a  bank  and  payable  at 
certain  other  banks  in  different  parts  of  the  country. 

The  charge  for  a  bank  money  order  is  usually  the  same  as  that  for  a  postal 
money  order. 


356 


PRACTICAL   BUSINESS   ARITHMETIC 


wmiiiwi/iiiiii/wwwiiiiitmiiiiiijwiijtiwi/iiiuwiiiiiiiiwuwiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiwii 


443.  A  telegraphic  money  order  is  a  telegram  of  an  express 
or  telegraph  company,  at  any  given  place,  ordering  the  pay- 
ment of  money  at  another  designated  place. 

THE  UNION  TELiLGRAPH  CO. 


INCORPORATED- 


23,000  OFFICES  IN  AMERICA 


CABLE  SERVICE  TO  ALL  THE  WORLD 


ROBERT  C.  CLOWRY,  President  and  General  Manager 


W  ti  IM  U  the  following  message  subject  to  the 
terms  on  back  hereof,  which  are  hereby  agreed  to. 

T-Q        The  Union  Telegraph  Co. 


Boston,    Mass.,    July  27, 


-19 


Rochester,    N.Y. 


Findable 
Findelkind 


Charles 


Osgood 


ten 


East 


Fichant 


The    Union    Telegraph    Co. 


These  telegrams  are  usually  in  cipher;  that  is,  in  a  language  not  under- 
stood by  those  who   are  unfamiliar  with    the    system   of    abbreviations 
(code)  used.     The  sender  and  the  receiver  must  each  have  a  code.     The 
following  code  will  illustrate  the  principle  of  telegraphing  in  cipher : 
Code  Word  Meaning 

Fichant  One  hundred  dollars 

Ficheron  One  thousand  dollars 

Findable  Please  pay of your  city  % . 

Findelkind  On  production  by  him  of  positive  evidence 

of  his  personal  identity. 
The  principle  of  a  telegraphic  money  order  is  the  same  as  that  of  a  postal 
money  order;  no  money  is  transferred  from  one  place  to  another.     The 
charge  for  an  order  is  usually  1%  of  the  amount  to  be  transmitted  plus 
twice  the  rate  for  a  single  ten-word  message. 


EXCHANGE  357 

The  following  are  the  rates  for  a  ten-word  message  from  Boston  to  the 
places  named : 

New  York        $0.30    '        Chicago  $0.50  Galveston     $0.75 

Philadelphia     $0.35  San  Francisco    $1.00  Rochester    $0.40 

ORAL  EXERCISE 

1.  What  was  the  total  cost  to  the  sender  of  the  postal 
money  order,  page  354?  the  express  money  order,  page  355? 
the  telegraphic  money  order,  page  356?  the  bank  money  order, 
page  356  ? 

2.  What  will  be  the  total  cost  of  a  postal  money  order  for 
27f?  $2.19?  i5.28?  $10.40?  $18.90?  $45.10?  $35.89?  $125 
($100-f-$25)?  $75.29?  $49.82?  $127.16? 

3.  What  will  be  the  total  cost  of  an  express  money  order  for 
$6.20?  $28.80?  $19.50?  $27.95?  $48.90?  $&5  ($504-$15)? 
$111?  $37.59?  $41.72?  $65.59?  $114? 

4.  What  will  be  the  total  cost  of  a  telegraphic  money  order 
from  Boston  to  New  York  for  $50?  $75?  $100?  $125?  $150? 
$200?  $300?  $400?  $450?  $500?  from  Boston  to  Phila- 
delphia? from  Boston  to  San  Francisco?  from  Boston  to 
Chicago  ? 

5.  Translate  the  following  telegraphic  money  order :  Find- 
able  F.  J.  Reed^  20  Park  St.  ficheron  findelkind.  How  much 
will  it  cost  for  such  an  order  from  Boston  to  Galveston?  from 
Boston  to  Chicago?  from  Rochester  to  Boston? 

WRITTEN  EXERCISE 

1.  Find  the  total  cost  of  5  postal  money  orders  for  the  fol- 
lowing amounts :  $3.10;  $8.19;  $25.06;  $18.50;  $20. 

2.  Find  the  total  cost  of  six  express  money  orders  for  the 
following  amounts :  $1.25;  $10;  $6.80;  $16.25;  $80;  $19.50. 

3.  Find  the  total  cost  of  the  following  telegraphic  money 
orders:  one  from  Boston  to  New  York  for  $50;  one  from 
Boston  to  Philadelphia  for  $500;  one  from  Boston  to  San 
Francisco  for  $175;  one  from  Boston  to  Galveston  for  $300; 
one  from  Boston  to  Rochester  for  $250. 


358 


PRACTICAL   BUSINESS   AEITHMETIC 


Checks  and  Bank  Drafts 

444.  Business  men  usually  keep  their  money  on  deposit  with 
a  commercial  bank  or  trust  company  and  make  most  payments, 
at  home  and  at  a  distance,  by  check;  that  is,  an  order  on  a 
bank  from  one  of  its  depositors  for  the  payment  of  money. 


Cfje  jfirst  Rational  Bank 


l^o.-^i^Z. 


W.-^^^ 


to  the  orl»cr  of  ^.^y^^p^-Z^-?:>^,^^^ 


i£^ 


n^z:^^^ 


SDoflaritf 


A  check  may  be  drawn  for  any  amount  so  long  as  it  does  not  exceed  the 
balance  on  deposit  to  the  credit  of  the  drawer.  It  may  be  drawn  payable 
to  :  (1)  the  order  of  a  designated  payee,  in  which  case  the  payee  must 
indorse  it  before  the  money  will  be  paid  over;  (2)  the  payee,  or  bearer,  in 
■which  case  any  one  can  collect  it ;  (3)  "  Cash,"  in  which  case  any  one  can 

collect  it. 

C.  B.  Sherman  &  Co.  and  E.  H. 
Robinson  &  Co.  in  the  foregoing 
check  both  reside  in  Boston.    On 
receiving  the  check,  E.  H.  Rob- 
inson &  Co.  indorse  it  and  de- 
posit  it   for   credit  with   their 
bank,  say  the  National  Shawmut 
Bank.    The  First  National  Bank 
and     the    National      Shawmut 
Bank,   as  well   as   each  of  the 
other   banks  in   the   city,    has 
many     depositors     who     draw 
INTERIOR  View  of  a  Clearing  House.       checks  upon  it   which   are    de- 
posited by  the  payees  in  various  other  city  banks,  and  it  also  receives  daily 
for  credit  from  its  own  depositors  checks  drawn  upon  various  other  city 
banks. 

Each  bank  therefore  has  a  daily  balance  to  settle  or  to  be  settled  with 
each  of  the  other  banks.  To  some  it  has  payments  to  make  and  from 
others  it  has  payments  to  receive.  If  these  balances  were  adjusted  in 
money,  each  bank  would  have  to  send  a  messenger  to  each  of  the  debtor 


EXCHANGE  359 

banks  to  present  accounts  and  receive  balances.  This  would  be  a  risky 
and  laborious  task.  To  facilitate  the  daily  exchanges  of  items  and  settle- 
ments of  balances  resulting  from  such  exchanges  there  has  been  established 
in  every  large  city  a  central  agency,  called  a  clearing  house.  This  agency 
is  an  association  of  banks  which  pay  the  expense  of  conducting  it  in  pro- 
portion to  the  average  amount  of  their  clearings. 

Suppose,  for  example,  that  the  banks  constituting  a  clearing  house  are 
Nos.  1,  2,  3,  and  4.  No.  1  presents  at  the  clearing  house  items  against  Nos. 
2,  3,  and  4,  and  Nos.  2,  3,  and  4  present  items  against  No.  1.  So,  likewise, 
with  No.  2  and  each  of  the  other  banks.  In  the  clearing  house  there  are  usually 
two  longitudinal  columns  containing  as  many  desks  as  there  are  banks  in  the 
association.  At  a  given  time  a  settling  clerk  from  each  bank  takes  his  place 
at  his  desk  inside  of  one  of  the  columns  and  a  delivery  clerk  from  each  bank 
takes  his  place  outside  the  column.  Each  delivery  clerk  advances,  one  desk 
at  a  time,  and  hands  over  to  each  settling  clerk  his  exchange  items  against  that 
bank.  After  the  circuit  of  the  desks  has 
been  completed  each  delivery  clerk  is  at 
the  point  from  which  he  started,  and  each 
settling  clerk  has  on  his  desk  the  claims  of 
all  of  the  other  banks  against  his  bank. 
Each  settling  clerk  then  compares  his 
claims  against  other  banks  with  those  of 
other  banks  against  him  and  strikes  a 
balance.  This  balance  may  be  in  favor 
of  or  against  the  clearing  house.  If  No.  1  brought  claims  against  Nos.  2,  3, 
and  4  aggregating  ^211,000  and  Nos.  2,  3,  and  4  brought  claims  against 
No.  1  aggregating  $200,000,  there  is  $11,000  due  No.  1  from  the  clearing 
house.  But  if  No.  1  brought  to  the  clearing  house  exchange  items 
aggregating  $200,000  and  took  away  exchange  items  aggregating  $211,000, 
there  is  $11,000  due  the  clearing  house  from  No.  1.  So,  likewise,  with 
No.  2  and  each  of  the  other  banks.  When  all  of  the  exchanges  have 
been  completed,  the  clearing  house  will  have  paid  out  the  same  amount 
that  it  has  received. 

But  all  checks  received  by  banks  are  not  payable  in  the  city.  Suppose 
that  A.  W.  Palmer,  of  Chicago,  111.,  owes  C.  B.  Andrews,  of  Westfield, 
Mass.,  $  500  and  that  the  amount  is  paid  by  a  check  on  the  City  National 
Bank  of  Chicago.  C.  B.  Andrews  receives  the  check  and  offers  it  for  credit  at 
the  Farmers  and  Traders  Bank  of  Westfield,  Mass.  The  Westfield  Bank  has 
no  account  with  any  Chicago  bank,  but  it  has  with  the  First  National  Bank 
of  Boston,  and  the  check  is  sent  to  that  bank  for  credit.  The  First  National 
Bank  wishes  *to  increase  its  New  York  balance  and  the  check  is  forwarded 
to  Chemical  National  Bank  of  New  York  for  credit.  Chemical  National 
Bank  next  mails  the  check  to  Commercial  National  Bank  of  Chicago,  the 


360  PRACTICAL   BUSINESS   ARITHMETIC 

bank  with  which  it  has  regular  dealings  in  that  city.  Commercial 
National  Bank  sends  the  check  to  the  clearing  house  and  it  is  carried 
to  the  City  National  Bank  by  a  messenger  from  that  bank.  Thus,  all  of  a 
depositor's  checks  will  in  time  be  presented  to  the  bank  on  which  they  are 
drawn.  When  presented,  they  will  be  charged  to  the  depositor,  cancelled,  and 
later  returned  to  him  to  be  filed  as  receipts. 

Banks  frequently  charge  their  depositors  a  small  fee  (rate  of  exchange) 
for  collecting  out-of-town  checks.  This  fee  is  rarely  over  ^jj  %,  but  there  is 
no  uniformity  in  the  matter.  Sometimes  when  a-  customer  keeps  a  large 
bank  account,  no  charge  whatever  is  made  for  the  collection. 

445.  It  often  happens  that  a  person  will  find  it  necessary  to 
make  payment  to  one  who  does  not  care  to  take  the  risk  of  a 
private  check  or  to  one  who  should  not  be  called  upon  to  pay 
the  cost  of  cashing  a  check.  In  such  cases  some  other  form  of 
instrument  of  transfer  must  be  used.  A  very  common  and  con- 
venient method  of  making  a  remittance  is  by  means  of  a  check 
of  one  banking  institution  upon  another  called  a  bank  draft. 

wMMMMjjz imiMMmiimmimmmmmMmmMmmiiJ' 


tjjosfon,  >^/rtass. 

Uraders  U\ational  njjank         J 

9?atf  to  tAe  order  ^f  """^  ""t^- ~(^  ^^^^^^^^-^^^^-^^ ^A^^M 


^^^?^-^^^-^-^  -r^y-^^^f^-g.^^^^^^^^^  — 9)oaa 


J\few    York  j  ^  <?-^' 


ten 


Banks  in  the  different  cities  frequently  keep  running  accounts  with  each 
other  and  make  periodical  settlements.  At  the  time  of  drawing  the  above 
draft  Traders  National  Bank  of  Boston  very  likely  has  checks  and  drafts 
drawn  upon  New  York  banks  which  it  has  received  from  its  depositors. 
These  it  sends  to  Chemical  National  Bank  to  cover  the  amount  of  the  draft. 
Corresponding  transactions  may  also  take  place  in  New  York.  Chemical 
National  Bank  may  sell  its  draft  on  Traders  National  Bank  and,  to  cover 
the  amount,  remit  checks  and  drafts  on  Boston  banks  which  it  has  received 
from  its  depositors.  What  is  occurring  between  the?  e  two  places  is  also 
occurring  between  all  manner  of  places ;  but  drafts  up  )n  New  York  banks 
and  other  financial  centers  are  the  most  used  in  makin/   remittances. 


EXCHANGE  361 

A  bank  draft  is  sometimes  drawn  payable  to  the  one  to  whom  it  is  to  be 
sent.  It  is  better,  however,  to  have  it  drawn  payable  to  the  purchaser  who 
may  indorse  it  over  to  the  person  to  whom  it  is  to  be  sent.  In  this  way 
the  name  of  the  sender  appears  on  the  draft,  and  when  canceled,  the  draft 
will  serve  the  purpose  of  a  receipt.  Banks  usually  sell  drafts  at  a  slight 
premium  on  the  face.  This  premium  is  called  exchange.  It  varies  somewhat 
(see  page  366),  but  is  seldom  more  than  ^^%. 

446.  There  are  still  other  methods  of  transmitting  funds 
through  the  instrumentality  of  a  bank.  A  depositor  may  ex- 
change his  own  check  for  that  of  a  cashier's  check.  The  latter, 
being  a  check  of  the  cashier  on  his  own  bank,  would  pass  among 
strangers  better  than  a  depositor's  check. 

Boston,  Mass.,       (kW.^^  /  r    19 No.diS^L£/ 

National  Shawmut  Bank 


%za^^^^ 


Dollars 


In  New  York  City  these  checks  are  occasionally  used  instead  of  the  New 
York  draft.  As  New  York  exchange  is  in  demand  in  all  parts  of  the 
country,  the  expediency  of  the  course  is  apparent. 

447.  By  depositing  a  sum  of  money  in  a  bank  a  person  may 
receive  a  certificate,  called  a  certificate  of  deposit.  This  will 
direct  the  payment  of  the  sum  deposited  to  any  person  whom 
the  depositor  may  name. 

'////////////j///.'///mmm//////mm^^^^^ 


f,SJ2J2j2J=-  Boston.  ,JLiss.,       (U^^^  //,./9 J^oJ^f 


-^atio/tiil  CtjLawmut  JSank 


payable  to  the  ortief  nf  '~'^/^.^^^^^Cl^^>^^  — " 

on  the  return  of  this  certificate  properly  indorsed. 


ea.     .^ —  ^jt; — 7f/~ —    /J 


The  payee  in  a  certificate  of  deposit  will  have  no  difficulty  in  getting  the 
certificate  cashed  or  the  amount  credited  to  him  by  his  bank. 


362  PRACTICAL  BUSINESS  ARITHMETIC 

ORAL  EXERCISE 

1.  Assuming  that  the  bank  which  cashed  the  check  on 
page  5  charged  ^  %  collection,  what  was  the  amount  credited 
to  the  depositor  ? 

2.  Silas  Long  of  New  York  deposited  the  following  check. 
The  bank  deducted  ^^  %  for  collection.  How  much  was  placed 
to  Silas  Long's  credit? 


%\^z  Virion  33anfe 


l^ar^to  ti^e  otDet  of. 


a. 


(?z'^C->^-<& 


:^^^^-<^i^^:^^ 


3.  B  deposited  three  out-of-town  checks  in  his  bank  as  fol- 
lows: $300;  1700;  $750.  If  the  bank  charged  ^0%  collec- 
tion, what  amount  was  placed  to  B's  credit? 

4.  Bring  to  the  class  a  number  of  canceled  checks  and  take 
several  of  them  and  trace  them  from  the  time  they  w^ere  issued 
until  they  were  filed  as  receipts  by  the  drawer.  Show  why  a 
canceled  check  is  the  best  kind  of  a  receipt  for  the  payment  of 
money  ? 

5.  How  much  did  the  bank  draft  on  page  360  cost  the  pur- 
chaser if  the  exchange  was  at  ^^o  %  premium  ? 

WRITTEN  EXERCISE 

1.  Find  the  cost  of  a  bank  draft  for  $3958.75  at  J^- %  pre- 
mium; of  a  bank  draft  for  $679.80  at  gV  %  premium;  of  a 
bank  draft  for  $768.54  at  50^  per  $1000  premium. 

2,  To  cover  the  cost  of  a  bank  draft  bought  at  ^0%  P^®" 
mium,  I  gave  my  bank  a  check  for  $250.25.  What  was  the 
face  of  the  draft  ?      What  was  the  rate  of  premium  per  $1000? 


EXCHANGE 


363 


3.  How  large  a  bank  draft  can  be  bought  for  $850.85,  ex- 
change being  at  -^q  %  premium  ? 

4.  Find  the  proceeds  of  the  accompanying  deposit,  ^^  %  col- 
lection and  exchange  being  charged  on  the  out-of-town  checks. 


When  the  receiving  teller  takes  a, 
deposit  from  a  customer,  he  classifies 
the  items  on  the  deposit  ticket,   as 
shown  in  the  accompanying  illustra- ' 
tion.    If  the  coin  and  bills  passed  in 
count  right,  these  items  are  checked  (V) 
on  the  deposit  slip ;  if  a  check  on  a 
clearing  house  bank  is  received,  it  is 
marked  with  the  number  of  that  bank ' 
in  the  clearing  house ;  if  a  check  on 
the   teller's    bank    is    received,    it   is 
marked  "B";  if  a  check  on  an  out-of- 
town  bank  is  received,  it  is  marked 
«X."  [ 


THE   UNION    NATIONAL   BANK 

DEPOSITED  SY 


Boston,. 


uyc^_^ 


/ 


■^^^^^ 


Specie  . 
Bills  .  . 
Checks  .   .  'sdCui^^.e^^^^  .    /^ 


t^o^-^SW^ i^ 


2l 


'.-ti<<.-rryj^ 


M, 


-,<^^ 


r^:^ 


-t//?A^^J/ 


^^<^i.^ 


^ty/o 


-^-^ 


e  ?  ^  ? 


12. 


5.  Write  a  bank  draft  using 
the  following  data :  your  ad- 
dress and  the  current  date;  drawer,  Central  National  Bank; 
drawee.  Chemical  National  Bank,  New  York;  amount,  $711.94; 
payee,  C.  E.  Denison;  cashier,  your  name.  How  large  a  check 
will  pay  for  the  draft  at  J^  %  premium  ?     Write  the  check. 

6.  Suppose  that  the  members  of  the  class  whose  surnames  be- 
gin with  the  letters  from  A  to  G  inclusive  have  a  deposit  Avith 
Traders  National  Bank  ;  that  the  members  whose  surnames 
begin  with  the  letters  from  H  to  N  inclusive  have  a  deposit 
with  City  National  Bank ;  that  the  members  whose  surnames 
begin  with  O  to  S  inclusive  have  a  deposit  with  First  National 
Bank;  and  that  the  members  whose  surnames  begin  with  T  to  Z 
inclusive  have  a  deposit  with  Central  Bank.  Let  each  student 
write  a  check  on  his  bank  in  favor  of  one  of  his  classmates, 
and  let  this  classmate  indorse  the  check  and  deposit  it  with  his 
bank.  Then  form  a  clearing  house,  strike  a  balance  between 
the  different  banks,  and  have  these  balances  adjusted  by  the 
payment  of  school  money. 


364  PEACTICAL   BUSINESS   ARITHMETIC 


Commercial  Drafts 

448.     Business  men  frequently  employ  the  commercial  draft 

as  an  aid  in  the  collection  of  accounts  that  are  past  due. 


. (^^^/^^^.^^^^  — — -^gy  to  the  order  of 


.  '^^^^■r^ryA^.^T^^^ ^^-^<^^J^^  "Z^.  — —  CD„//„^ 


Value  received  and  charge  to  account  of 
So,    (^^^g^^^gg- 

J/^..Al/^S)ue. 


/2r 


^ 


The  above  is  a  commoii  form  of  draft  used  for  collection  purposes. 
Edgar  McMickle  owes  Wilbert,  Closs  &  Co.  %  260.50.  The  amount  is  due, 
and  Wilbert,  Closs  &  Co.  draw  a  draft  on  Edgar  McMickle  and  leave  it  with 
their  Springfield  bank  for  collection.  The  Springfield  bank  forwards  it  to 
its  correspondent  in  Paterson  and  this  bank  sends  it  by  messenger  to  Edgar 
McMickle.  When  he  pays  the  draft,  the  Paterson  bank  notifies  the  Spring- 
field bank,  and  that  bank  deducts  a  small  fee  (collection  and  exchange)  for 
collecting  the  draft,  and  credits  Wilbert,  Closs  &  Co.  for  the  proceeds. 

449.  It  has  been  seen  (page  327)  that  the  time  draft  is  fre- 
quently used  in  connection  with  sales  of  merchandise. 


C^:=yA^^-^y  .gZ^g>g^:U</  ^.^^yy.^^^^^C<-:Z^^  <7^n,j  to  the  order  of 

.C^^^^^^.^^^^  — ■  — 

Value  received  and  charge  to  account  of 


Suppose  Quincy,  Bradley  &  Co.  sell  L.  B.  Wade  &  Co.  a  bill  of  merchan- 
dise amounting  to  $500.  Terms:  30-da.  draft  for  the  amount  of  the  bill. 
The  draft,  as  above,  and  the  bill  in  regular  form  would  be  drawn  up  and 


EXCHANGE  •  365 

sent  to  L.  B.  Wade  &  Co.  for  acceptance.  The  object  of  drawing  a  time 
draft  in  connection  with  sales  of  merchandise  is  twofold  :  (1)  when  ac- 
cepted, the  draft  serves  as  a.  written  contract;  (2)  since  an  acceptance  is 
negotiable,  it  may  be  discounted  and  cash  realized  upon  it  before  maturity. 
Such  a  draft  is  frequently  left  with  a  bank  for  collection  instead  of  being 
remitted  with  the  bill.  The  bank  will  then  first  present  the  draft  for  accept- 
ance and  later  for  payment. 

ORAL  EXERCISE 

1.  If  you  exchange  your  check  for  a  cashier's  check,  is  there 
any  charge  for  the  accommodation  ? 

2.  If  the  sight  draft  on  page  364  was  collected  by  a  bank 
which  charged  ^%  collection,  how  much  was  placed  to  the 
credit  of  Wilbert,  Closs  &  Co.? 

3.  You  deposited  in  Shawmut  National  Bank  $5000,  received 
the  certificate  of  deposit  shown  on  page  361,  and  remitted  it 
to  E.  B.  Stanton  on  account.      Would  there  be  any  exchange  ? 

WRITTEN  EXERCISE 

1.  The  draft  on  page  364  was  accepted  July  17,  and  dis- 
counted July  25.  If  the  bank  charged  J^  %  collection  and 
6  %  interest,  how  much  was  placed  to  the  credit  of  the  drawers  ? 

2.  Mar.  27  Wilson  Bros.,  Chicago,  111.,  drew  a  30-da.  draft 
on  E.  W.  King,  Toledo,  O.,  in  favor  of  themselves,  payable  30  da. 
after  date,  for  13500,  and  mailed  it  for  acceptance.  Apr.  1  the 
draft  was  received  accepted;  Apr.  2  it  was  discounted  at  City 
Bank.  If  the  charges  were  ^q%  collection  and  6%  interest, 
what  amount  was  credited  to  Wilson  Bros.? 

3.  Apr.  17  O.  H.  Brooks,  Buffalo,  N.Y.,  drew  a  sight  draft 
on  Slocum  &  Co.,  Hartford,  Conn.,  in  favor  of  himself,  for  $391, 
and  left  it  with  his  bank  (First  National)  for  collection.  First 
National  Bank  sent  the  draft  to  its  Hartford  correspondent 
(Commercial  National),  and  5  da.  later  informed  O.  H.  Brooks 
that  the  draft  had  been  collected,  and  the  amount,  less  |  %  col- 
lectio.n,  placed  to  his  credit.  If  O.  H.  Brooks's  bank  balance 
was  $758.62  before  the  draft  was  drawn,  what  was  it  after  the 
draft  was  credited  ?    Write  the  draft  and  show  the  indorsements. 


366  PRACTICAL   BUSINESS  ARITHMETIC 

4.  Aug.  9  you  sold  C.  D.  Mead  &  Co.,  San  Francisco,  Cal., 
39  mahogany  sideboards  at  $162.50,  delivered  the  goods  to  the 
Interstate  Transportation  Co.,  and  received  a  through  bill  of 
lading  (receipt  for  the  goods  and  an  agreement  to  transport 
and  deliver  them  to  the  consignee  or  to  his  order).  You  then 
drew  a  sight  draft  on  C.  D.  Mead  &  Co.  in  favor  of  your  bank, 
attached  the  draft  to  the  bill  of  lading,  and  left  it  with  your 
bank  for  collection.  Your  bank  indorsed  the  draft  and  the  bill 
of  lading  and  sent  them  to  First  National  Bank  of  San  Fran- 
cisco for  collection  and  credit.  Aug.  23  you  received  advice 
that  the  draft  had  been  collected,  and  the  amount,  less  J  %, 
placed  to  your  credit.    What  was  the  amount  credited  ? 

When  First  National  Bank  of  San  Francisco  received  the  draft,  it  notified 
C.  D.  Mead  &  Co.  They  paid  the  draft,  and  the  bank  gave  them  the  bill  of 
lading.  When  goods  are  shipped  in  this  manner,  the  transportation  company 
will  not  deliver  the  goods  until  the  consignee  presents  the  bill  of  lading. 

Fluctuation  of  Rates  of  Exchange 

450.  It  has  been  seen  that  money  orders  always  sell  for  more 
than  their  face  value,  and  that  bank  drafts  frequently  cost  a 
little  more  than  their  face  value.  When  exchange  costs  its 
face  value,  it  is  said  to  be  at  par ;  when  it  costs  more  than  its 
face  value,  it  is  said  to  be  at  a  premium ;  when  it  costs  less  than 
its  face  value,  it  is  said  to  be  at  a  discount. 

On  bank  drafts  for  small  snms,  say  ^  500  or  less,  exchange  is  usually  at 
a  uniform  premium.  This  premium  is  to  pay  the  banks  for  their  trouble 
and  the  expense  of  shipping  money  to  the  centers  on  which  the  drafts  are 
drawn,  when  balances  at  these  points  become  low.  But  exchange  on  the 
trade  centers  of  the  country  may  be  at  par  at  one  time,  at  a  premium  at 
another,  and  at  a  discount  at  still  another.  For  example,  during  the  late 
fall  months,  when  the  grain  crops  begin  to  be  sent  East,  New  York  is  send- 
ing a  great  many  checks  and  drafts  to  the  section  of  which  Chicago  is  the 
trade  center.  Exchange  on  New  York  is  then  very  plentiful  in  Chicago,  and 
if  a  man  in  Chicago  wished  to  buy  a  draft  on  New  York  for  a  large  amount, 
say  1 10,000  or  more,  the  Chicago  banks  will  sell  it  to  him  at  a  discount. 
But  if  a  man  in  New  York  at  that  time  wished  to  buy  a  draft  on  Chicago 
for  110,000,  he  would  have  to  pay  a  premium,  because  the  New  York 
banks  would  be  anxious  not  to  decrease  their  Chicago  balances. 


EXCHANGE  367 

Early  in  the  spring,  when  New  York  importers  and  jobbers  are  sending 
foreign  and  domestic  manufactured  goods  for  distribution  in  the  West,  a 
great  many  checks  and  drafts  are  being  sent  from  the  West  to  New  York,  and 
exchange  is  at  a  discount  in  New  York  and  at  a  premium  in  Chicago.  This 
principle  applies  at  all  trade  centers  between  which  exchange  operations  go 
on.  Smaller  places  make  their  settlements  in  or  through  larger  places,  and 
the  main  exchange  transactions  go  on  between  the  few  leading  cities,  with 
converging  lines  on  New  York, 

The  rate  of  exchange  between  two  cities  will  never  exceed  the  cost  of 
shipping  actual  money  from  one  of  the  cities  to  the  other,  except  in  time  of 
panic  or  a  financial  unrest.  Thus  when  the  cost  of  sending  money  by  express 
from  New  York  to  Chicago  is  $5  per  $  10,000,  the  discount  in  New  York  or 
the  premium  in  Chicago  will  not  greatly  exceed  ^^%  ($5  per  1 10,000). 
To  prevent  the  rates  from  going  any  higher  the  banks  will  arrange  for  the 
shipment  of  actual  money  from  New  York  to  Chicago. 

As  a  rule  no  charge  is  made  for  cashing  bank  drafts  on  the  trade  centers 
of  the  country,  like  New  York,  Chicago,  and  Philadelphia. 

451.  It  has  been  seen  that  banks  frequently  charge  a  small 
fee  for  collecting  paper  payable  out  of  town. 

In  some  cases  the  rates  of  collection  are  more  or  less  arbitrary ;  in  others 
they  are  governed  by  trade  movements,  the  same  as  rates  of  exchange.  In 
still  others  the  clearing  house  association  fixes  the  rate. 


ORAL   EXERCISE 

Find  the  cost  of  the  following  hank  drafts: 

1.  $18,500  at  2V  %  discount ;  at  40^  per  $1000  premium. 

2.  1516.90  at  yL%  premium  ;  at  50^  per  #1000  discount. 

3.  11600.80  at  75^  per  $1000  premium  ;  at  ^V  %  discount. 

4.  A  draft  for  $4000  was  bought  for  13998.  Was  ex- 
change at  a  premium  or  at  a  discount,  and  what  rate  ? 

5.  J.  E.  Smith  &  Co.  drew  at  sight  on  E.  M.  Barrows  for 
$250  and  made  collection  through  their  bank.  If  the  bank 
charged  J^  %  for  collection,  for  what  amount  did  J.  E.  Smith 
&  Co.  receive  credit  ? 

6.  During  the  late  fall  many  checks  and  drafts  are  being 
sent  to  the  southern  cities  in  payment  for  shipments  of  cotton. 
At  such  times  is  exchange  on  New  York  likely  to  be  at  a  dis- 
count or  at  a  premium  in  New  Orleans  ?  in  New  York  ? 


368 


PEACTICAL   BUSINESS   ARITHMETIC 


7.  Frank  M.  Burton  wishes  to  collect  an  account  of  8  70.58 
and  for  this  purpose  draws  the  following  draft  and  leaves  it 
with  the  National  Express  Co.  for  collection.  If  the  express 
company  charges  25^  for  collection,  how  much  will  it  collect 
of  Fred  W.  Greenlaw  ?  how  much  will  it  pay  Frank  W. 
Burton  ? 


^JMJLj^i^^ 


Note  that  the  draft  contains  the  clause  "  With  current  rate  of  Exchange." 
This  means  that  the  drawee  is  requested  to  pay  the  face  of  the  draft  plus 
the  cost  of  exchange.  Nearly  all  express  companies  have  arrangements  by 
which  they  undertake  the  collection  of  notes  and  accounts.  The  process  of 
collecting  is  simple.  The  note  or  draft  covering  the  amount  of  the  account 
is  placed  in  a  collection  envelope  furnished  by  the  express  company,  and  sent 
to  its  destination.  If  collection  cannot  be  made,  notice  is  given  with  reasons 
for  refusal ;  if  collection  is  made,  the  money  is  sent  back  in  the  collection 
envelope,  and  the  amount,  less  collection  charges,  paid  to  the  one  for  whom 
the  collection  was  undertaken.     The  charge  varies  with  the  distance. 


WRITTEN  EXERCISE 

1.  A  bank  draft  for  815,000  was  bought  for  $14,992.50. 
Was  exchange  at  a  premium  or  at  a  discount,  and  what  rate  ? 
At  this  rate  find  the  cost  of  a  draft  for  117,121.98  ;  a  draft  for 
112,929.75  ;  a  draft  for  $127,162.89. 

2.  I  gave  the  American  Express  Co.  an  account  of  $178.50 
for  collection.  If  the  collection  charges  were  $  2.50  per  $1000, 
how  much  did  I  receive  from  the  company?  At  this  rate  what 
should  be  the  proceeds  from  the  collection  of  three  drafts  with 
amounts  as  follows  :  $125.60  ;  $218.90  ;  and  $134.50  ? 


EXCHANGE 


369 


3.  An  agent  sold  for  me  1000  T.  hay  at  $17.50  per  ton. 
He  paid  il25  for  cartage,  $75  for  storage,  charged  2|^  com- 
mission, and  remitted  the  proceeds  by  a  bank  draft  bought  at 
^  f)  premium.      What  was  the  face  of  the  draft  ? 

4.  A  Boston  commission  merchant  sold  for  his  principal  in 
Chicago  27,518  lb.  leather  at  25  |J^  per  pound.  If  he  charged  a 
commission  of  4^  %,  how  large  a  bank  draft,  bought  at  $1.50 
per  $1000  premium,  should  he  remit  to  his  principal  ? 

5.  Mar.  8  Edward  Whitman  &  Co.  drew  a  draft  payable 
30  da.  after  date  on  El  wood  &  Spears  for  $375.98  and  had  it 
discounted  at  City  Bank.  If  the  rate  of  collection  was  ^% 
and  interest  5  % ,  what  were  the  proceeds  of  the  draft  ? 

6.  Copy  and  complete  the  following  letter  of  advice, 
assuming  that  the  rate  of  collection  is  ^%  on  Nos.  720  and 
716,  and  -^-^%  on  Nos.  692  and  710.     Check  the  results. 


National  Exchange  Bank 


Mr.      £/iUd^,   10.    ^'. 

Vic 


Albaxy,  N.Y 
,       Cashicr 


'9 


Dear  Sir,  —  We  credit   your  account   this  day   for  the  proceeds   of 
collections   as   stated   below.  Respectfully   yours, 

L.    H.    PiERSox,    Cashier 


PROCEEDS 


>>n    I  ^^  (( 


tl 


90(' 


jLu'-  I  i  u 


8760    50  \ 
8  '^500  I  00  I 


oo 

^-  ip  'H:  '■<•      I     ■%■  --K- 


370  PRACTICAL   BUSINESS  ARITHMETIC 

FOREIGN  EXCHANGE 

Foreign  Money 

oral  exercise 

1.  Repeat  the  table  for  English  money ;  for  French  money ; 
for  German  money.    (See  Appendix  B,  page  451.) 

2.  What  is  the  value  of  a  pound  sterling  in  United  States 
money  ?  of  a  franc  ?  of  a  mark? 

3.  Express  $4866.50  in  English  money;  ^100  in  United 
States  money.  Express  $  1930  in  French  money  ;  1000  fr.  in 
United  States  money.  Express  $238  in  German  money; 
10000  M.   in  United  States  money. 

A  pound  sterling  is  commonly  thought  of  as  about  $5;  a  shilling  or  a 
mark  as  about  25  f ;  a  penny  as  about  2  ^ ;  a  franc  or  lira  as  about  20  )^ ;  a 
guilder  as  about  40  f .     In  problems  4-6  use  these  approximations. 

4.  Express  $100  as  English  money;  as  German  money; 
as  French  money;  1500  guilders  in  United  States  money. 

5.  Express  as  United  States  money  :  X 15  ;  £8  5s.  ;  £25 
10s.;    100  M.;   1500  M.  ;   1750  M.  ;   75  fr.  ;   350  fr.  ;   200  fr. 

6.  A  and  B  while  abroad  spent  3  wk.  in  Naples,  Italy.  If 
their  expenses  here  averaged  25  lire  apiece  per  day,  how  much 
was  this  in  United  States  money  for  the  3  wk.  ? 

WRITTEN  EXERCISE 

1.  Express  as  pounds  and  decimals  of  a  pound  :  X25  6s. ; 
£150  15s.;   X200  10s.  6d.;  X  300  12s.  9c?. 

2.  Reduce  to  United  States  money  :  X25  10s.  ;  X120  9s. 

3.  Reduce  to  United  States  money:  275  M.;  1500  M.  75  pf.; 
315  fr.;  725  fr.;  X115  10s.  6d.  Reduce  $1250  to  English 
money ;  to  French  money  ;  to  German  money. 

4.  In  a  recent  year  the  funded  debt  of  the  German  Empire 
amounted  to  2,733,500,000  M.,  of  which  1,240,000,000  M.  bore 
interest  at  3|%  and  1,493,500,000  M.  at  3%.  Express  in 
United  States  money  the  interest  on  the  funded  debt  for  1  yr. 


j:xchange 


371 


The  Metric  System 

452.  The  metric  system  is  a  system  of  measures  having  a 
decimal  scale  of  relation.  It  was  invented  by  France,  and  is 
now  used  in  practical  business  in  a  large  part  of  the  civilized 
world.  It  has  been  authorized  by  law  in  Great  Britain  and 
the  United  States,  but  is  not  generally  used  in  these  countries 
except  in  foreign  trade  and  in  scientific  investigations. 

The  principal  units  of  the  system  are  the  meter  for  length,  the  liter  for 
capacity,  and  the  gram  for  weight.  Submultiples  and  multiples  of  these 
units  are  easily  learned  when  the  meaning  of  the  prefixes  is  known.  The 
Latin  prefixes,  deci,  centi,  and  milli  mean  respectively  0.1,  0.01,  and  0.001  of 
the  unit.  The  Greek  prefixes  deca,  hekto,  kilo,  and  myria  mean  respectively, 
10,  100,  1000,  and  10,000  times  the  unit. 


Table  of  Length 


10  millimeters  (mm.) 

10  centimeters 

10  decimeters 

10  meters 

10  dekameters 

10  hektometers 

10  kilometers 


1  centimeter  (cm.)  = 
=  1  decimeter  (dm.)  = 
=  1  meter  (m.)  = 

=  1  dekameter  (Dm.)      = 
=  1  hektometer    (Hm.)  = 
=  1  kilometer  (Km.)         = 
=  1  myriameter  (Mm.)  =  10,000 
The  units  in  common  use  are  indicated  by  black-faced  type. 
Table  of  Square  Measure 


.01 

.  meter. 

.1 

meter. 

1. 

meter. 

10. 

meters. 

100. 

meters. 

000. 

meters. 

,000. 

meters. 

.0001  sq.  meter. 
.01  sq.  meter. 
1 .    sq.  meter  =  1  centare. 

sq.  meters  =  1  are. 

sq.  meters  =lhectare. 

sq.  meters. 

sq.  meters. 


100  sq.  millimeters  =1  sq.  centimeter  (sq.  cm.) 

100  sq.  centimeters  =1  sq.  decimeter  (sq.  dm.) 

100  sq.  decimeters    =1  sq.  meter  (sq.  m.) 

100  sq.  meters  =1  sq.  dekameter  (sq.  Dm.)  =  100. 

100  sq.  dekameters  =1  sq.  hektometer  (sq.  Hm.)=  10,000. 

100  sq.  hektometers=l  sq.  kilometer  (sq.  Km.)     =     1,000,000. 

100  sq.  kilometers    =1  sq.  myriameter  (sq.  Mm.)  =100,000,000. 

The  centare,  are  (a.),  and  hektare  are  common  terms  in  land  measure- 
ments. 

Table  of  Cubic  Measure 

1000  cu.  millimeters 
1000  cu.  centimeters 
1000  cu.  decimeters 
1000  cu.  meters 
1000  cu.  dekameters 
1000  cu.  hektometers 
1000  cu.  kilometers 

The  cubic  meter  is  also  called  a  stere,  a  unit  used  in  measuring  wood. 


cu.  centimeter  (cu.  cm.)         = 

.000001 

cu. 

m. 

1  cu.  decimeter  (cu.  dm.)       = 

.001 

cu. 

m. 

1  cu.  meter  (cu.  m.)                = 

1. 

cu. 

m. 

1  cu.  dekameter  (cu.  Dm.)    = 

1000. 

cu. 

m. 

1  en.  hektometer  (cu.  Hm.)  = 

1,000,000. 

cu. 

m. 

1  cu.  kilometer  (cu.  Km.)      = 

1,000,000,000. 

cu. 

m. 

1  cu.  myriameter  (cu.  Mm.)  = 

1,000,000,000,000. 

cu. 

m. 

;72 


PRACTICAL   BUSINESS   ARITHMETIC 


Table  of  Capacity 

10  milliliters 

(ml.) 

=  1  centiliter  (cl.) 

= 

.01  liter. 

10  centiliters 

=  1  deciliter  (dl.) 

= 

.1    liter. 

10  deciliters 

'=  1  liter  (1.) 

:=. 

1.      liter. 

10  liters 

=  1  dekaliter  (DL) 

- 

10.      liters. 

10  dekaliters 

=  1  hektoliter  (HI.) 

= 

100.      liters. 

10  hektoliters 

=  1  kiloliter  (Kl.) 

= 

1000.      liters. 

A  liter  is  the  same  as  a  cubic  decimeter. 


Table  of  Weight 


10  milligrams  (mg.)  =  1  centigram  (eg.) 


10  centigrams 
10  decigrams 
10  grams 
10  dekagrams 
10  hektograms 
10  kilograms 
10  myriagrams 
10  quintals 


=  1  decigram  (dg.) 
=  1  gram  (g.) 
=  1  dekagram  (Dg.) 
=  1  hektogram  (Ilg.) 
=  1  kilogram  (Kg.) 
=  1  myriagram  (Mg.) 
=  1  quintal  (Q.) 
=  1  tonneau  (T.) 


.01  gram. 


.1 

gram. 

1. 

gram. 

10. 

grams. 

100. 

gi-ams. 

1000. 

grams 

=       10,000. 

grams. 

=    100,000. 

grams. 

=  1,000,000. 

grams 

The  tonneau  is  usually  called  a  metric  ton. 


Table  of  Approximate  Values 


A  meter 

=  3i  ft.  or  1 

1  yd.        A  stere              =  y\  cd. 

A  kilometer 

=  f  mi. 

A  gram             =  15|  gr. 

A  square  meter 

=  14  sq.  rd. 

A  kilogram      =  2i  lb.  ay. 

An  are 

=  4  sq.  rd. 

A  liter               =  1  qt. 

An  hectare 

=  2|  A. 

An  hektoliter  =  2^  bu. 

A  cubic  meter 

=  1.3  cu.  yd. 

A  meti-ic  ton    =  2200  lb. 

ORAL  EXERCISE 

1.  Name  the  prefix  which  means  10,000;  0.001;  100;  0.01; 
10;  0.1;  1000. 

2.  Read  the  following:  2.5m.;  72  mm.;  95.5  cm.; 
302.05  km.  Express  475.125  m.  in  millimeters  ;  in  hek- 
tometers. 

3.  Which  of  the  divisions  of  the  following  scale  are 
millimeters?  centimeters? 


0 

1 

2 

3 

■4 

5 

6 

7 

8 

y 

,:o 

1 1 1 1 

III! 

1 

: 

1  decimeter 


excha:^ge  ,  373 

4.  A  certain  tower  is  200  in.  high;  this  is  approximately 
how  many  feet? 

5.  How  many  square  meters  in  1  a.  ?  how  many  ares  in 
5  Ha.  ?  in  25  Ha.  ? 

6.  How  many  liters  in  1  cu.  m.?  in  5  cu.  m.?  Find  the 
cost  of  5  Kl.  of  milk  at  5)^  a  liter  ;  at  4^  a  liter. 

7.  Find  the  length  of  your  schoolroom  in  meters;  the 
weight  of  any  familiar  object  in  kilograms. 

8.  Bought  1000  m.  of  cloth.      How  many  yards  was  this  ? 

9.  An  importer  bought  1000  1.  of  liquors  at  80^  a  liter.  If 
he  sold  it  at  13.50  per  gallon,  did  he  gain  or  lose,  and  how  much? 

10.    The  distance  from  Paris  to  Cologne  is  510  Km.;   from 
Cologne  to  Mainz  150  Km.     Express  these  distances  in  miles. 

WRITTEN  EXERCISE 

1.  At  $  75  an  acre  find  the  cost  of  75  Ha.  of  land. 

2.  Find  the  cost  of  175.75  m.  of  lace  at  65^  a  meter. 

3.  How  many  steres  of  wood  in  a  pile  12  m.  long,  1.5  m. 
wide,  and  3  m.  high?     How  many  cords? 

4.  A  merchant  bought  cloth  at  $1.14  per  meter,  including 
duties.     For  how  much  must  he  sell  it  per  yard  to  gain  33^%? 

5.  I  imported  1000  m.  of  silk  dress  goods  (see  duties,  page 
294)  at  10  fr.  per  meter  and  sold  it  at  $  3  per  yard.  Did  I  gain 
or  lose  and  how  much,  the  silk  being  1  yd.  wide  ? 

6.  The  distance  between  two  places  on  a  map  is  15.5  cm. ; 
this  is  - — i— --  of  the  actual  distance.  What  is  the  actual  dis- 
tance in  miles? 

7.  C  bought  cloth  at  $2  per  meter,  including  duties,  and 
sold  it  by  the  yard  at  a  gain  of  25%.  What  was  the  selling 
price  per  yard? 

8.  The  speed  rate  of  a  certain  express  train  is  64  Km.  an 
hour ;  of  a  certain  mail  train,  48  Km.  an  hour.  In  a  journey  of 
384  Km.  what  time  will  be  saved  by  taking  the  express  instead 
of  the  mail  train. 


374  PKACTICAL  BUSINESS   ARITHMETIC 

Foreign  Money  Orders 

453.  Small  sums  are  frequently  sent  from  one  country  to 
another  by  means  of  foreign  money  orders. 

The  international  postal  money  order  and  the  foreign  express  money  order 
or  check  are  both  extensively  used  for  this  purpose.  These  orders  are 
usually  drawn  payable  in  the  money  of  the  country  on  which  they  are  issued. 
They  are  similar  in  form  to  domestic  money  orders,  but  are  issued  on  prac- 
tically the  same  principle  as  the  ordinary  bank  draft. 

ORAL  EXERCISE 

1.  D  in  Chicago  wishes  to  send  E  in  Havre,  France,  780  fr. 
At  19.5^  to  the  franc,  how  large  an  express  money  order  (in 
U.S.  money)  can  he  buy  ? 

2.  B  in  New  York  wishes  to  send  $120  to  C  in  Leipzig, 
Germany.  At  24^  to  the  mark,  how  large  an  express  money 
order  (in  marks)  can  he  buy  ? 

3.  At  1%  premium  find  the  cost  of  an  international  money 
order,  payable  in  Great  Britain,  for  each  of  the  following 
amounts:  |40;  $50;  175;  1100;  $150;   1200. 

4.  A  in  Boston  bought  an  international  money  order  for 
$20  and  sent  it  to  a  friend  in  Liverpool,  England.  At  1% 
premium,  what  did  the  order  cost?  For  how  many  pounds 
sterling  (approximately)  was  it  issued  ? 

WRITTEN  EXERCISE 
e 

1.  I  wish  to  send  $100  to  G  in  Holland.  At  40^^  to  the 
guilder,  how  large  an  express  money  order  can  I  buy  ? 

2.  I  wish  to  send  $50  to  a  friend  in  Scotland.  At  $4.87  to 
the  pound,  how  large  an  express  money  order  can  I  buy  ? 

3.  C  in  Chicago  sent  D  in  Geneva  an  express  money  order 
for  256.41  fr.  At  19.5^  to  the  franc,  how  much  did  the  order 
cost  C  ? 

4.  E  in  Philadelphia  sent  F  in  Naples  an  international  postal 
money  order  for  128.21  lira.  At  19.5^  to  the  lira,  how  much 
did  the  order  cost  E  ? 


EXCHANGE  375 


Bills  of  Exchange 

454.   Drafts  of  a  person  or  a  bank  in  one  country  on  a  person 
or  a  bank  in  another  country  are  usually  called  bills  of  exchange. 


fe^^  JUL  !Q,1915l 


B     ^nSriA-l 


455.  Bills  of  exchange  may  be  divided  into  three  classes: 
(1)  bankers'  bills,  which  are  drawn  by  one  banker  upon  an- 
other ;  (2)  commercial  bills,  which  are  drawn  by  one  mer- 
chant upon  another ;  (3)  documentary  bills,  which  are  drawn 
by  one  merchant  upon  another  and  secured  by  the  assignment 
and  transfer  of  a  bill  of  lading  and  policy  of  insurance  covering 
merchandise  on  its  way  to  the  market. 

Theforegoing  form  is  a  bankers'  demand  draft  or  check. 

Bankers'  bills  of  exchange  are  frequently  issued  in  duplicate ;  that  is,  in 
sets  of  two  of  like  tenor  and  amount.  These  bills  are  sometimes  sent  by 
different  mails;  but  more  frequently  the  original  is  sent  and  the  duplicate 
is  placed  on  file  to  be  sent  in  case  of  necessity.  Duplicate  bills  are  so  con- 
ditioned that  the  payment  of  one  of  them  cancels  the  other.  The  bankers' 
sole  bill  of  exchange  is  also  used.  This  is  preferred  by  many,  inasmuch  as 
it  may  be  more  easily  negotiated  by  the  payee  when  he  resides  in  a  city  other 
than  the  one  drawn  upon.  Commercial  and  documentary  bills  of  exchange 
are  usually  issued  in  duplicate. 

456.  The  mint  par  of  exchange  is  the  actual  value  of  the 
pure  metal  in  the  monetary  unit  of  one  country  expressed  in 
terms  of  another. 


376  PRACTICAL   BUSINESS   ARITHMETIC 

The  mint  par  of  exchange  is  determined  by  dividing  the  weight  of  pure 
gold  in  the  monetary  unit  of  one  country  by  the  weight  of  pure  gold  in  the 
monetary  unit  of  another.  Thus,  the  United  States  gold  dollar  contains 
23.22  troy  grains  of  pure  gold  and  the  English  pound  sterling,  113.0016  troy 
grains.  113.0016  h-  23.22  =  4.8665.  Since  there  is  4.8665  times  as  much  pure 
gold  in  the  pound  sterling  as  in  the  gold  dollar,  the  pound  sterling  is  worth 
4.8665  times  $1,  or  f  4.8665.  The  mint  par  of  exchange  is  used  mainly  in 
determining  the  values  on  which  to  compute  customs  duties. 

457.  The  rate  of  exchange  is  the  market  value  in  one 
country  of  the  bills  of  exchange  on  another. 

The  price  paid  for  bills  of  exchange  fluctuates.  When  the  United  States 
owes  Great  Britain  exactly  the  same  amount  that  Great  Britain  owes  the 
United  States,  the  debts  between  these  countries  can  be  paid  without  the 
transmission  of  money,  and  exchange  is  at  par.  But  w'hen  Great  Britain 
owes  the  United  States  a  greater  amount  than  the  United  States  owes 
Great  Britain,  exchange  in  the  United  States  is  at  a  discount  and  in  Great 
Britain  at  a  premium,  and  vice  versa.  The  rates  of  premium  or  discount 
are  limited  by  the  cost  of  shipping  gold  bullion  from  one  country  to  another. 
The  cost  of  shipping  gold  from  New  York  to  London  is  about  f  %.  There- 
fore, when  A  in  New  York  owes  B  in  London,  and  A  cannot  buy  a  bill  of 
exchange  on  London  for  less  than  $4.88^  to  $4.89,  it  is  cheaper  for  him  to 
export  gold.  On  the  other  hand,  if  D  in  l^ondon  owes  C  in  New  York  and 
C  cannot  sell  a  draft  on  D  for  more  than  |4.83|  to  $4.84,  it  is  cheaper  for 
him  to  import  gold.  The  greater  part  of  exchange  is  drawn  on  Great 
Britain,  France,  Germany,  Holland,  Belgium,  and  Switzerland.  Because 
London  is  the  financial  center  of  the  world,  probably  more  foreign  exchange 
is  drawn  on  Great  Britain  than  on  all  the  other  countries  combined. 

458.  Exchange  on  Great  Britain  is  usually  quoted  at  the 
number  of  dollars  to  the  pound  sterling ;  exchange  on  France, 
Belgium,  and  Switzerland,  at  the  number  of  francs  to  the  dollar  ; 
exchange  on  Germany,  at  the  number  of  cents  to  each  four  marks; 
exchange  on  Holland,  at  the  number  of  cents  to  each  guilder. 

The  accompanying  foreign  exchange  rates  were  quoted  recently. 
In   Great   Britain    3    da.   of  60  Days   Demand 

grace    are  allowed  on    all  bills       GennalyrreiciismarksV/////////////.%?y8       *'953| 


gxa^c    aic    aiiuwcu    uii    an    uxiia        Germany,  reichsmarks 947/8 

drawn  payable  after  sight,  but      gg^Yum ^'^*"''' .' " *5i sf 

drafts  on  Great  Britain  payable      Switzerland,  francs 5.I884      5.15% 

^     .    ,^  T  11  Holland,  guilders 40  40% 

at  sight  or  on  demand  have  no 

grace.     There  are  no  days  of  grace  allowed  on  any  drafts  drawn  on  Germany, 

and  nearly  all  Europe,  excepting  Holland,  where  1  da.  of  grace  is  allowed. 


EXCHANGE 


377 


WRITTEN  EXERCISE 

1.  Using  the  foregoing  table  of  quotations,  or  current  quota- 
tions clipped  from  any  daily  newspaper,  find  the  cost  of  de- 
mand drafts  for  each  of  the  following  amounts  : 

a.  £100.  d.  160  guilders.  g.  200  M.  j.  6000  M. 
h.  X1200.  e.  240  guilders.  h.  160  M.  k,  4000  M. 
c.    £1800.      /.     1200  guilders.      ^.    2000  M.        I.    12000  M. 

2.  Find  the  cost  of  a  60-da.  draft  for  each  of  the  amounts 
in  problem  1. 

WRITTEN  EXERCISE 

1.  F.  M.  Cole  &  Co.,  importers,  Boston,  owe  Richard  Roe, 
London,  £525  10s.,  6J.,  buy  by  check  the  draft  illustrated  on 
page  375,  and  remit  it  in  full  of  account.  If  exchange  on 
London  is  ^4. 87 J,  what  was  the  amount  of  the  check  ? 

2.  Jordan,  Marsh  &  Co.  wish  to  import  a  quantity  of  woolen 
goods  from  Bradford,  England.  They  make  up  an  order  and 
inclose  in  payment  the  following  draft  which  they  buy  by 
check,  at  $4.85 J.     What  was  the  amount  of  the  check  ? 

f  BKOfWBHOTHERS&CO    :^^^^H 


I  %Sfioo  — 


'M^ 


f         3ttESS9?BROTI^,SlIIHJEir&CO.  /7^  ^^^ 

4       JVb._3497___  VcgSOQf^. 


Brother3  ^  Co. 


3.  45  da.  before  the  draft  was  due  (problem  2)  John  Smith 
&  Co.  sold  it  to  Baring  Bros,  at  2%  discount.  How  much 
(in  English  money)  did  they  receive  ?  Write  the  indorsements 
which  Would  appear  on  the  back  of  the  draft. 


37 


PEACTICAL   BUSINESS  ARITHMETIC 


4.    D.  M.  Knowlton  &  Co.  drew  the  following  commercial 
:  exchange  and  sold  it  to 
How  much  was  received  for  it  ? 


bill  of  exchange  and  sold  it  to  Kidder,  Peabody  &  Co.  at  96| 


Commercial  bills  of  exchange  are  usually  drawn  by  exporters  against 
funds  abroad  which  have  accumulated  to  their  credit  from  sales  previously 
made.  The  exporter  generally  waits  until  the  rates  of  exchange  are  high 
and  then  draws  the  draft  as  above. 

5.  Aug.  1  T.  H.  Reed  &  Co.,  exporters,  Minneapolis,  Minn., 
bought  through  their  broker,  24,000  bu.  No.  1  wheat  at  84^  per 
bushel  and  paid  for  same  by  check.  What  was  the  amount  of 
the  check,  the  broker's  commission  being  J  ^  per  bushel  ? 

6.  Aug.  2  the  wheat  was  delivered  and  placed  with  City 
Elevator  for  storage.  The  storage  rates  were  |^  per  bushel  for 
the  first  10  da.  or  fraction  thereof,  and  -^^j^  per  bushel  for 
each  additional  day  thereafter.  On  Aug.  15  tlie  wheat  was 
withdrawn  from  the  City  Elevator  and  delivered  to  the  Soo 
Freight  Line  for  shipment  to  W.  B.  Radclitfe  &  Son,  Liver- 
pool.    What  was  the  amount  of  the  storage  bill  ? 

7.  The  wheat  was  sold  to  W.  B.  Radcliffe  &  Son  at  £1 12s. 
2d,  per  quarter  (8  bu.  or  480  lb.).  Make  out  the  bill  under 
date  of  Aug.  15. 

8.  On  Aug.  15  a  through  bill  of  lading  in  duplicate  was  re- 
ceived from  the  Soo  Freight  Line.  If  the  through  freight  rate 
from  Minneapolis  to  Liverpool  was  2d.  per  hundredweight, 
what  was  the  amount  of  the  freight  bill  ? 


EXCHANGE 


379 


9.  Aug.  16,  upon  presentation  of  the  bill  of  lading  to  the 
Western  Assurance  Co.,  the  goods  were  insured  for  10%  more 
than  their  billed  value  and  a  certificate  of  insurance  issued. 
What  was  the  amount  of  the  premium,  the  rate  being  1J%  ? 
10.  T.  H.  Reed  &  Co.,  drew  the  following  draft  on  W.  B. 
Radcliffe  &  Son  and  attached  it  to  the  bill  of  lading  and  cer- 
tificate of  insurance.  These  documents,  which  constitute  what 
is  called  a  documentary  bill  of  exchange,  were  then  offered  for 
sale  and  later  sold  to  Kidder,  Peabody  &  Co.,  at  the  rate  of 
H.84|  per  pound.     How  much  was  received  for  the  bill? 


sold    the    draft   to 


11.  Aug.    17    Kidder,  Peabody   &    Co 
American  Express  Co.  at  f4.84J.     If  the  American  Express 
Co.  paid  by  check,  what  was  the  amount  of  the  check? 

12.  American  Express  Co.  forwarded  the  bill  to  Provincial 
Bank,  Liverpool,  for  collection,  and  this  bank  presented  the 
draft  to  W.  B.  Radcliffe  &  Son  for  acceptance.  Sept.  1  the 
wheat  arrived  by  steamer  and  as  the  draft  was  stamped  "Sur- 
render documents  only  upon  payment  of  draft"  W.  B.  Rad- 
cliffe &  Son  had  to  pay  the  draft  before  they  could  get  the  docu- 
ments or  the  goods.  As  the  draft  has  47  da.  yet  to  run,  the 
bank  allowed  W.  B.  Radcliffe  &  Son  1%  discount.  What  was 
the  amount  paid  by  W.  B.  Radcliffe  &  Son  ? 

Such  drafts  are  frequently  stamped  "Surrender  documents  upon  accept- 
ance of  the  draft."  In  such  cases  the  documents  would  be  delivered  to  the 
consignee  upon  the  acceptance  of  the  draft,  and  he  could  then  obtain  pos- 
session of  the  goods. 


380 


PRACTICAL  BUSINESS   ARITHMETIC 


13.    What  was  T.  H.  Reed  &  Co.'s  net  gain  or  loss  on  the 
transactions  in  problems  5-10  ? 


Letters  of  Credit  and  Traveler's  Checks 

459.  A  traveler's  letter  of  credit  is  an  instrument  issued  by  a 
banker  instructing  his  correspondents  in  specified  places  to  pay 
the  holder  funds  in  any  amount  not  exceeding  a  specified  sum. 


ULAIl  LETTER  OF  C 

^i?*/B  13.683 


ClRCULAIl  LETTER  OF  CREDIT 


^  ckkw-^Ua^.^JufuAt  2l^y0/S 


%A 


I  123  J^llMall.L 


-^X/t-a-T-^O^rr-ii-xCstx'^-w^ 


NDON; 


^a^i^c 


'Messrs  BROWN,  S  H I PLEY.^  Co. 


'cnTiyOuleJote'  Ou/ytiL'  30  ' — 


^yony 


ec/^ 


/o^/.2.oo-/ 


EXCHANGE 


381 


The  purchaser  of  a  letter  of  credit  is  required  to  subscribe  his  name 
upon  the  document  as  a  means  of  identification  later  on.  Other  copies 
of  the  signature  are  left  and  forwarded  to  the  leading  foreign  banks 
drawn  upon.  When  the  traveler  desires  funds,  he  presents  his  letter  to  the 
proper  bank  at  the  place  in  which  he  is  stopping.  The  letter  itself  always 
specifies  the  banks  that  will  honor  the  draft.  When  the  letter  is  presented 
to  a  foreign  banker  for  payment,  he  draws  a  sight  draft  on  the  London 
banker,  which  draft  the  traveler  is  required  to  sign.  If  the  signatures  on 
the  letter  and  on  the  draft  are  identical,  the  amount  desired  is  promptly  paid 
and  indorsed  on  the  back  of  the  letter.  The  indorsements  on.  the  back 
of  a  letter  show  at  all  times  the  balance  available  for  the  traveler.  The 
bank  making  the  last  payment  retains  the  letter  to  send  to  the  drawee 
in  London.  Letters  of  credit  are  usually  drawn  payable  in  pounds  ster- 
ling, but  they  are  paid  in  the  current  money  of  the  country  in  which 
they  are  negotiated.  Banks  usually  charge  1%  commission  for  issuing 
a  letter  of  credit. 

460.  Another  instrument  frequently  used  by  travelers  is 
what  is  called  a  traveler's  check. 


When  a  check  is  purchased,  the  buyer  signs  bis  name  in  the  upper  left- 
hand  corner.  When  he  wishes  funds,  he  presents  his  check  to  the  cor- 
respondent of  the  express  company  or  bank  and  signs  his  name  either 
in  the  upper  left-hand  corner  or  on  the  back  of  the  check.  On  the  form 
above,  he  would  sign  his  name  in  the  lower  left-hand  corner;  but 
on  the  form  on  page  382  he  would  sign  his  name  on  the  back.  The  lat- 
ter form  is  considered  better  because  it  is  more  diflBcult  to  forge  an- 
other's signature  when  there  is  no  signature  near  at  hand  from  which  to 
copy. 

The  terms  of  issue  are  cash  for  the  face  amount  plus  1%  commission. 


382 


PEACTICAL   BUSINESS   AEITHMETIC 


ORAL  EXERCISE 

1.  At  $4.85  to  the  pound  sterling  plus  1%  commission,  what 
did  the  letter  of  credit  on  page  380  cost? 

2.  At  the  same  rate,  find  the  cost  of  a  letter  of  credit  for 
^500;   XIOOO. 

3.  At  1%  commission,  what  will  be  the  total  cost  of  10 
checks  like  the  sample  on  page  381?  of  20  checks?  of  25 
checks  ? 

4.  At  f  4.85  to  the  pound  plus  |  %  commission,  what  was  the 
cost  of  a  traveler's  check  on  page  382  ?  of  a  book  of  10  checks 
like  the  sample  on  page  382  ? 


WRITTEN  EXERCISE 

1.  On  the  letter  of  credit,  page  380,  the  following  payments 
are  recorded  on  the  back :  Aug.  31,  c£  200 ;  Sept.  9,  <£  400 ; 
Oct.  15,  X  250 ;  Nov.  1,  X  100 ;  Nov.  12,  £  200.  The  holder 
returns  to  New  York  on  Nov.  20  and  presents  the  letter  to 
Brown  Brothers  &  Co.  for  the  refund.  At  S4.85  to  the  pound, 
how  much  Avill  Brown  Brothers  &  Co.  pay  on  the  letter? 

In  this  problem  it  is  assumed  that  Brown  Bros.  &  Co.  refund  1  %  commis- 
sion on  the  unused  portion  of  the  letter. 


EXCHANGE 


383 


2.  At  25^  per  word  and  1%  of  the  amount,  find  the  cost  of 
a  twenty -one  word  cable  money  order  from  Boston  to  Paris  for 
25,000  fr.  when  exchange  is  quoted  at  5.15|. 

Money  may  be  cabled  from  one  country  to  another  on  the  same  principle 
that  it  is  telegraphed  from  one  part  of  any  country  to  another  part.  In  a 
cable  message  a  charge  is  made  for  each  word  in  the  address  of  the  one  to 
whom  it  is  sent. 

WRITTEN  REVIEW  EXERCISE 

1.  A  broker  sold  for  me  a  bill  on  Manchester,  England,  at 
f  4.84i  and  charged  |%  brokerage.  What  was  the  face  of  the 
bill,  if  the  proceeds  were  $5218.50? 

2.  How  much  remains  in  the  bank  to  the  credit  of  H.  B. 
Claflin  &  Co.  after  the  following  check  was  issued  ? 


Bn.JAj2 


amount.  $ 


^liamfii  Cru£(t  Company 

to  tf>e  otUrr  iA^&n<^fr^t^^^,i^^-n^J>^  / ,' ,'  F  -^ 


l'£yL^tY--'^-^'<^'!^(^^''^- 


^^^  *  *   *  ^^aWoWat^ 


>^,>^H^^ 


3.  My  agent  in  Brussels,  Belgium,  purchased  for  me  carpet 
amounting  to  35,000  fr.,  and  his  commission  was  5%.  I  re- 
mitted him  a  draft  to  cover  the  cost  of  the  carpet  and  the 
commission  for  buying.  K  exchange  was  5.15|,  and  I  paid  for 
the  draft  by  check,  what  was  the  amount  of  the  check? 

4.  My  agent  in  Rotterdam  sold  for  me  525  kegs  of  tobacco, 
each  containing  50  lb.,  at  J  guilder  per  pound,  and  charged 
me  a  commission  of  41%.  I  drew  on  him  for  the  proceeds  and 
sold  the  draft  to  a  broker  at  40|.  If  the  broker  charged  |% 
for  his  services,  what  did  I  receive  as  proceeds  of  the  draft  ? 


EQUATIONS   AND   CASH  BALANCE 
CHAPTER   XXXI 

EQUATION  OF  ACCOUNTS 
ORAL  EXERCISE 

1.  How  long  will  it  take  1 5  to  produce  the  same  interest  as 
$10  for  10  da.  ?  ,  The  use  of  $100  for  1  mo.  is  equivalent  to 
what  sum  for  2  mo.  ? 

2.  If  I  have  the  use  of  150  of  A's  money  for  30  da.,  how 
much  of  my  money  should  he  have  the  use  of  for  15  da.  in 
return  for  the  accommodation  ? 

3.  The  interest  on  $40  for  2  mo.  plus  the  interest  on  $40  for 
4  mo.  is  equal  to  the  interest  on  $80  for  how  many  months  ? 

4.  D  owes  E  $100;  $50  is  due  in  2  mo.  and  the  balance  in 
4  mo.  In  how  many  months  may  the  whole  be  paid  without 
loss  to  either  party  ? 

5.  On  Apr.  1  I  bought  a  bill  of  goods  amounting  to  $200, 
payable  as  follows:  $100  in  3  mo.  and  the  balance  in  5  mo. 
In  how  many  months  may  the  whole  sum  be  equitably  paid  ? 

6.  A  owes  B  $400  and  pays  $200  30  da.  before  the  account 
is  due.  How  long  after  the  account  is  due  may  B  have  in 
which  to  pay  the  balance  ? 

461.  The  process  of  finding  the  date  on  which  the  settle- 
ment of  an  account  may  be  made  without  loss  of  interest  to 
either  party  is  called  equation  of  accounts. 

Sometimes  one  or  more  of  the  items  in  a  personal  account  are  not  paid  at 
maturity  and  the  holder  of  the  account  suffers  a  loss ;  sometimes  one  or 
more  of  the  items  are  paid  before  maturity  and  the  holder  of  the  account 
realizes  a  gain.  To  equitably  adjust  these  items  of  loss  and  gain,  accounts 
are  equated.  Retail  accounts  are  not  often  equated ;  but  wholesale  and 
commission    accounts   are  frequently   equated,   particularly   foreign    ones. 

384 


EQUATION  OF  ACCOUNTS 


385 


462.  The  time  that  must  elapse  before  several  debts,  due  at 
different  times,  may  be  equitably  paid  in  one  sum  is  called  the 
average  terin  of  credit ;  the  date  on  which  payment  may  be 
equitably  made,  the  average  date  of  payment,  the  equated 
date,  or  the  due  date. 

463.  Any  assumed  date  of  settlement  with  which  the  several 
dates  in  the  account  are  compared  for  the  purpose  of  deter- 
mining the  actual  due  date  is  sometimes  called  the  focal  date. 

The  face  value  of  each  item  should  always  be  used  in  equating  accounts. 
Items  not  subject  to  a  term  of  credit  and  interest-bearing  notes  are  worth 
their  face  value  on  the  day  they  are  dated.  Items  subject  to  a  term  of 
credit  and  non-interest-bearing  notes  are  not  worth  their  face  value  until 
maturity. 

SIMPLE   ACCOUNTS 


ORAL  EXERCISE 

1.  If  I  owe  $200  due  Jan.  1  and  |400  due  Jan.  31,  when 
may  both  accounts  be  equitably  paid  in  one  sum  ? 

Solution.  On  Jan.  31,  there  is  legally  due  $600  -f  $  1  (the  interest  on  $200 
for  30  da.).  Since  more  than  the  face  of  the  account  is  due,  the  equitable  date 
of  settlement  is  before  Jan.  31.  It  will  take  $600  one  third  as  long  as  $200  to 
produce  $  1  interest,  i  of  30  da.  =  10  da.  The  whole  account  may  therefore 
be  paid  10  da.  before  Jan.  31,  or  Jan.  21,  without  loss  to  either  party. 

2.  You  sold  Baker,  Taylor  &  Co.  goods  as  follows  :  Apr.  20, 
1600;  Apr.  30,  $600.  How  mucli  is  legally  due  on  the  ac- 
count Apr.  30  ?  On  what  day  may  the  whole  account,  i  1200, 
be  paid  without  interest  ? 

3.  When  is  the  following  account  due  by  equation  ? 

A.  B.  Comer . 


19— 
Sept. 


To  mdse. 
To  mdse. 


300 
300 


4.  Rowland  &  Hill  bought  goods  of  you  as  follows  :  Oct.  16, 
$400;  Oct.  31,  $800.  How  much  was  legally  due  on  the  ac- 
count Oct.  31  ?  On  what  date  can  the  whole  of  the  account, 
$  1200,  be  paid  without  interest  ? 


386 


PKACTICAL   BUSINESS   ARITHMETIC 


464.    Example.     On  what  date  may  the  total  of  the  following 
account  be  paid  without  interest  ? 


F.  M.  Pratt  & 

Co. 

19- 

Jan. 

1 

9 

15 

21 

26 

To  mdse. 
To  mdse. 
To  mdse. 
To  mdse. 
To  mdse. 

30 
120 
150 
300 

60 

00 

Solution.  Take  the  latest  date, 
Jan.  26,  as  the  focal  date.  If  settle- 
ment was  made  on  Jan.  26,  the 
holder  of  the  account  might  charge 
interest  on  each  item  as  shown  in 
the  accompanying  statement. 

The  holder  loses  $0.11  per  day 
as  long  as  the  account  remains  un- 
settled. If  settlement  was  made 
Jan.  26,  the  loss  would  be  $  0.99,  or 
9  days'  interest;  therefore  if  the  ac- 
count were  settled  9  da,  before  Jan. 
26,  the  holder  would  lose  nothing. 


Date 

Amount 

Days 

Interest 

Jan.      1 

130 

25 

i.125 

9 

120 

17 

.34 

15 

150 

11 

.275 

21 

300 

5 

,25 

26 

60 

0 

$660 


1.99 


The  amount  of  the  account  =  $  660. 
The  interest  on  $660  for  1  da.  =  $0.11. 
$  0.99  -=-  $  0.11  =  9,  or  the  number  of  days. 
Jan.  26—9  da.  =  Jan.  17,  the  equated  date. 


Proof.  The  proof  of  the  problem  must  show  that  the  interest  on  the  items 
dated  before  Jan.  17^  the  equated  date,  is  offset  by  the  discount  on  the  items 
dated  after  Jan.  17.     The  following  items  are  dated  before  Jan.  17  : 


Date 

Interest 
Period 

Item 

[nterest 

Jan.    ltol7 

16  da. 

$30 

$.08 

9  to  17 

8 

120 

.16 

15  to  17 

2 

160 

.05 

Total  interest 

$.29 

nng  items  are 

dated  after  Jan. 

17: 

Date 

Discount 
Period 

Item 

Discount 

Jan.  17  to  21 

4  da. 

$300 

$.20 

17  to  26 

9 

60 

.09 

Total  discount,  $  .29 

The  proof  shows  that  the  equated  date,  Jan.  17,  is  correct. 

Any  rate  of  interest  may  be  used  in  equating  an  account.  As  a  matter 
of  convenience,  always  use  6  %.  If  items  are  subject  to  terms  of  credit,  add 
the  time  to  the  date  of  the  items  before  beginning  to  equate. 


EQUATION   OF  ACCOUNTS 


387 


WRITTEN  EXERCISE 


In  each  of  the  following  problems  find  the  equated  date   and 
prove  the  work.     Assume  that  all  the  dates  are  in  1916. 


1.    F.  M.  Drake,  Di 
Mar.  2,  To  mdse. 

8,  To  mdse. 
11,  To  mdse. 
17,  To  mdse. 

23,  To  mdse. 
3.    Geo.  M.  Barton,  Dr. 
Aug.  3,  To  mdse.,  60  da.  1360. 

6,  To  mdse.,  30  da.     240. 

11,  To  mdse.,  30  da. 

19,  To  mdse.,  30  da. 

24,  To  mdse.,  30  da. 
5.    Carter  &  Co.,  Dr. 
May  5,  To  mdse. 

12,  To  mdse. 

16,  To  mdse. 

20,  to  mdse. 

23,  To  mdse. 
1\    Brigham  &  Co.,  Dr. 

Sept.  4,  To  mdse.,  60  da.  $600. 

9,  To  mdse.,  60  da.     450. 

12,  To  mdse.,  60  da. 

17,  To  mdse.,  60  da. 
22,  To  mdse.,  30  da. 

30,  To  mdse.,  net, 
9.    Brown,  Kerr  &  Co.,  Dr. 
Oct.  1,  To  mdse.,  3  mo.  |210 

5,  To  mdse.,  60  da.    840 

13.  To  mdse.,  60  da.    720 

21,  To  mdse.,  60  da. 

24,  To  mdse.,  60  da. 

31,  To  mdse.,  net, 


1120. 

180. 

60. 

240. 

150. 


300. 
60. 

180. 

1180. 
300. 
230. 
270. 
360. 


350. 
400. 
500. 
150. 


2.    Louis  M.  Allen,  Dr. 
Apr.  3,  To  mdse.     .     .    $160. 
9,  To  mdse.     .     .       250. 

13,  To  mdse.     .     .      100. 

19,  To  mdse.     .     .      280. 

23,  To  mdse.     .     .      420. 
4.    Leon  H.  Hazelton,  Dr. 
June  6,  To  mdse.     . 


9,  To  mdse.     .     .      300. 

14,  To  mdse.     .     .      400. 

24,  To  mdse.     .     .      600. 

27,  To  mdse.     .     .      330. 
6.  Lamson  &  Roe  Co.,  Dr. 
Dec.  1,  To  mdse.,  3  mo.  1 294.20. 

10,  To  mdse.,  3  mo.    698.40. 

20,  To  mdse.,  60  da.  136.60. 

24,  To  mdse.,  60  da.  740.60. 
28,  To  mdse.,  60  da.  700.40. 

8.    D.  H.  Beckwith  &  Co.  Dr. 
Nov.  3,  To  mdse.,  2  mo.  1 750.50. 
8,  To  mdse.,  2  mo.    432.25. 

17,  To  mdse.,  net,      275.50. 

22,  To  mdse.,  2  mo.    210.50. 

25,  To  mdse.,  1  mo.    168.30. 
28,Tomdse.,lmo.    240.50. 

10.    D.  M.  Smith  &  Co.,  Dr. 


660. 
540. 
300. 


July  3,  To  mdse. 
8,  To  mdse. 
11,  To  mdse. 
16,  To  mdse. 
25,  To  mdse. 
29,  To  mdse. 


$420.30. 
325.70. 
417.25. 
186.24. 
240.60. 
126.84. 


PEACTICAL   BUSINESS  ARITHMETIC 


COMPOUND  ACCOUNTS 


ORAL  EXERCISE 

1.    The  following  is  your  account  with  John  D.  Foster. 


Had  no  payment  been  made,  when  would  the  account  have  been  due? 
Smce  no  payment  was  made  until  after  maturity,  you  have  lost  the  use 
of  $  400  for  how  many  days  ?  To  offset  this  loss  what  should  be  the  date  of 
an  interest-bearing  note  given  to  cover  the  balance  of  the  account?  Jan. 
16  — 30  da.  =  Dec.  ?,  the  date  of  an  interest-bearing  note  given  to  cover 
the  balance  of  the  account. 

2.   The  following  is  your  account  with  Walter  H.  Wood. 
Walter  H.  Wood 


19— 
Apr. 


Tomdse.,30da. 


600 


00 


19— 

Apr. 


16 


By  Cash 


300 


00 


Had  no  payment  been  made,  when  would  the  account  have  matured? 
By  the  payment  recorded  you  have  gained  the  use  of  $300  for  how  many 
days  ?  To  offset  this  gain,  you  should  allow  Walter  H.  Wood  to  keep  the 
balance  of  the  account  how  many  days  after  maturity?  May  1  +  15  da. 
=  May  ?,  the  date  on  which  the  balance  is  equitably  due. 

3.  May  1  B  sold  C  goods  amounting  to  I  500.  Terms  :  30 
da.  May  11  C  made  a  payment  of  $  250  on  account.  On 
what  date  is  the  balance  of  the  account  due  ? 

4.  Find  the  date  of  an  interest-bearing  note  given  for  the 
balance  of  each  of  the  following  accounts,  assuming  that  the 
terms  in  each  case  are  30  da.;  assuming  that  the  terms  are  cash. 


Name 

a.  H.  H.  Howard 

b.  W.  H.  Lyman  &  Co. 

c.  R.  H.  Delaney  &  Son 


Dr. 

Jan.  1,  $400 
Jan.  1,  $400 
Jan.  1,  $400 


Cr. 

Jan.  16,  1 300 
Jan.  16,  $  100 
Jan.  16,  1 200 


EQUATION   OF  ACCOUNTS  389 

465.    Examples,    l.    Find  the  equated  date  for  the  following  : 


y^^<r'y^3<?'V'e6<d..£^. 


J  Co 


II  '9— 


/3^-^XZ.^^'^ 


Solution.  Take  as  focal  date  the  latest  date  in  the  account,  Feb.  24. 

Debits 


Date 

Items 

Interest 
Periods 

Interest 

Feb.  1 

$360 

23  da. 

$1.38 

14 

240 

10 

.40 

$600 

Credits 

•      $1.78 

Date 

Items 

Interest 
Periods 

Interest 

Feb.  18 

$180 

6  da. 

$.18 

24 

180 
$360 

0 

.00 

$.18 

$  600  -  $  360  =  $  240,  the  balance  of  the  account.  $  1.78  -  $  .18  =  $  1.60, 
the  interest  due  the  holder  of  the  account  on  Feb.  24.  The  interest  on  $240 
for  1  da.  =:  $0.04.  $  1.60  h-  $0.04  =  40,  the  number  of  days.  If  the  account 
were  settled  Feb,  24  there  would  be  interest  for  40  da.  due  the  holder  of  it. 
Therefore  the  balance  of  the  account  is  due  40  da.  before  Feb.  ^4.  Feb.  24  — 
40  da.  =  Jan.  15,  the  equated  date. 

Proof.  To  prove  the  correctness  of  the  above  work  it  is  necessary  to  show 
that  a  payment  of  $240  on  Feb.  24  will  result  in  no  loss  of  discount  to  either 
party.     This  may  be  done  by  equating  the  account,  using  Jan.  15  as  the  focal  date. 

Debits 


Date 

Discount 
Periods 

Jan.  15  to  Feb.  1 

17  da. 

15  to         14 

30 

Date 

Credits 

Discount 
Periods 

Fan.  15  to  Feb.  18 

34  da. 

15  to           24 

40 

Items 

Discount 

$360 

$1.02 

240 

1.20 

$600 

$2.22 

Items 

Discount 

$180 

$1.02 

180 
$360 

1.20 

$2.22 

As  there  is  no  difference  between  the  debit  discount  and  the  credit  discount, 
the  account  is  proved  to  be  due  by  equation  on  Jan.  15,  19 — . 


390 


PRACTICAL   BUSINESS  ARITHMETIC 


2.    Find  the  equated  date  for  the  following  account 


^.,^tr>'y?^.'f:Cd■.^^.icl■tC<l': 


JO    , 

ye  . 


J  J  a 


Solution. 


Date 

Apr.  1 
24 
30 


A.ssuine 

May  31  to  be  the  date  oi  settlement. 

Debits 

Term  of 

Credit 

Maturity 

Item 

Interest 
Period 

Interest 

60  da. 

May  31 

$660 

Oda. 

$.00 

30 

24 

360 

7 

.42 

10 

10 

280 
$1300 

21 

.98 
$1.40 

Credits 

Date 

Item 

Interest 
Period 

Interest 

May  2 

$330 

29  da. 

$1,595 

20 

300 
$630 

11 

.55 
$2,145 

$  1300  -  $630  =  $670,  the  balance  of  the  account, 
the  interest  due  Watson  &  Moore  on  May  31.  The  interest  on  $670  for  1  da.  = 
$0.11^.  $0.745 -^  $0.11 1  =  6.6  or  7,  the  number  of  days.  If  the  account  were 
settled  May  31,  Watson  &  Moore  might  deduct  $0.75  from  the  balance  of  the  ac- 
count ;  therefore  the  balance  of  the  account  is  not  due  until  7  da.  after  May  31, 
or  June  7,19 — . 

Proof.     The  maturity  of  each  item  is  used  in  the  proof. 


Datb 


May  31  to  June  7 


24  to 
10  to 


Debits 

Interest 
Period 

7  da. 
14 

28 


Item 

$660 
360 

280 


Interest 

$  .77 
.84 
1.307 


$1300 

$2,917 

Credits 

Datb 

May  2  to  June  7 
20  to           7 

Interest 
Period 

36  da. 

18 

Item 

$330 

300 

Interest 
$1.98 
.90 

$630  $2.88 

$2,917  —  $2.88  =  $0,037  ;  as  this  is  less  than  the  interest  on  the  balance  of 
the  account  for  \  da.  the  solution  is  probably  correct. 


EQUATION    OF   ACCOUNTS 


391 


WRITTEN  EXERCISE 

Find  the  equated  date  and  prove  the  work: 
1.  Fred'L.  Upson 


Jan. 


To  mdse. 
To  mdse. 


360 
240 


19— 
Jan. 
Feb. 


By  cash 
By  cash 


2. 


Vinton  L.  Brown  &  Co. 


180 
120 


10— 

Mar. 
Apr. 


To  mdse. 
To  mdse. 
To  mdse. 
To  mdse. 


420 
300 

300 
120 


Id- 
Mar. 

Apr. 


By  cash 
By  cash 
By  cash 


3. 


Anson  L.  James 


540 
180 
300 


10— 





10— 



Mar. 

8 

To  mdse.,  10  da. 

240 

60 

Mar. 

18 

By  cash 

240 

60 

12 

To  mdse.,  10  da. 

180 

30 

24 

By  30-da.  note 

19 

To  mdse.,  10  da. 

246 

with  interest 

300 

29 

To  mdse.,  10  da. 

381 

24 

31 

By  cash 

257 

54 

The  charge  under  Mar.  8  was  paid  when  due,  Mar.  18.     Such  items  may 
be  omitted  in  equating  the  account. 


4. 

MacGreg 

OR   & 

Co. 

10— 

19— 

Apr. 

7 

To  mdse.,  10  da. 

127 

54 

Apr. 

17 

By  cash 

127 

54 

25 

To  mdse. 

218 

99 

30 

By  cash 

100 

May 

6 

To  mdse.,  10  da. 

87 

43 

May 

16 

By  cash 

206 

42 

18 

To  mdse. 

150 

24 

By  mdse. 

35 

20 

27 

To  mdse.,  10  da. 

86 

45 

5. 

David  J. 

Upe 

[AM 

10— 

^9^^ 

June 

7 

To  mdse. 

128 

50 

June 

14 

By  cash 

332 

50 

10 

To  mdse. 

432 

75 

25 

By  mdse. 

67 

40 

15 

To  mdse. 

78 

55 

30 

By  cash 

248 

60 

!21 

To  mdse. 

246 

80 

July 

15 

By  cash 

500 

;  29 

To  mdse. 

312 

30 

28 

By  mdse. 

88 

54 

July 

3 
14 

To  mdse. 
To  mdse. 

186 
66 

40 

36 

1 

392 


PRACTICAL   BUSINESS   ARITHMETIC 


ACCOUNT   SALES 

466.  The  method  of  averaging  an  account  sales  is  practically 
the  same  as  the  method  of  averaging  an  ordinary  ledger  ac- 
count. The  charges  for  freight,  commission,  guaranty,  etc., 
constitute  the  debits  and  the  sales  the  credits  of  the  account. 

Commission  and  guaranty  are  sometimes  considered  due  on  the  date  of 
the  last  sale,  and  sometimes  on  the  average  date  of  the  sales.  When  goods 
are  sold  promptly,  commission  and  guaranty  are  generally  considered  due  on 
the  date  of  the  last  sale ;  when  the  sales  are  large  and  there  are  long  intervals 
between  them,  commission  and  guaranty  are  generally  considered  due  on 
the  average  due  date  of  the  sales.  When  goods  are  sold  for  cash,  the  ac- 
count sales  is  seldom  averaged. 

WRITTEN   EXERCISE 

1.  Equate  the  account  sales  on  page  271,  assuming  that 
both  sales  were  made  on  30  days'  time,  and  that  the  commission 
is  due  on  the  date  of  the  last  sale. 

2.  Copy  and  complete  the  following  account  sales.  Consider 
the  commission  as  due  on  the  date  of  the  last  sale. 


Buffalo,  N.Y., 


July  3, 


19 


Sale  for  the  account  of  Wentworth,   Stratton  &  Co. 

Indianapolis.    Ind. 

By  C.  M.  Ettenheimer  &  Sons 

Commission  Merchants 


Sales 

June 

8 

295  bbl.  Roller  Process  Flour, 

60  da. 

$5.75 

**«#»» 

12 

315  *•  Old  Grist  Mill  Flour, 

Cash 

5.45 

*»»*,»* 

July 

1 

305  '*  Roller  Process  Flour, 

60  da. 

5.67  1/2 

««** 

** 

3 

285  "  Old  Grist  Mill  Flour. 
Charges 

30  da. 

5.75 

*«*» 

** 

June 

12 
9 

Freight  and  cartage 
Insurance 

112 
60 

50 

July 

3 
3 

» 

Storage 

Commission.  5%   of  sales 

Net  proceeds  due  by  equation 

30 

** 

«*»* 

**»« 

** 

CHAPTER  XXXII 
CASH  BALANCE 

ORAL  EXERCISE 

1.    When  is  the  balance  of  the  following  account  due  ? 
James  B.  Sweeney 


Jan. 


To  indse.,  30  da. 


600  00 


19- 
Jan. 


31 


By  cash 


300 


00 


2.  If  no  interest  is  charged  on  overdue  balances,  how  much 
will  settle  the  account  Feb.  28  ? 

3.  If  interest  at  6%  is  charged  on  all  amounts  not  paid  at 
maturity,  what  is  the  cash  balance  of  the  above  account  Feb.  28  ? 

4.  Assuming  that  interest  is  charged  on  amounts  not  paid 
at  maturity,  find  the  cash  balance  of  the  above  account  March 
30,  at  6%. 

467.  The  amount  due  upon  an  account  at  any  given  time  is 
called  the  cash  balance  of  an  account. 

When  interest  is  not  charged  and  discount  is  not  allowed,  the  cash 
balance  is  the  difference  between  the  sides  of  an  account.  When  interest  is 
charged  and  discount  is  allowed,  the  cash  balance  is  the  difference  between 
the  sides  of  an  account  after  interest  has  been  added  to  overdue  items  and 
discount  deducted  from  items  not  yet  due. 

Whether  or  not  interest  or  discount  is  charged  or  allowed  on  ledger 
accounts  is  determined  by  custom  or  agreement.  It  is  customary  for 
wholesalers  to  charge  interest  on  all  overdue  accounts.  As  a  rule,  retailers 
do  not  charge  interest  on  the  items  of  an  overdue  account,  but  they  fre- 
quently close  personal  accounts  at  the  end  of  the  year  and  charge  interest 
on  the  balances  brought  down  from  the  date  of  closing  to  the  date  of 
settlement. 

468.  Example.  What  is  the  cash  balance  of  the  following 
account  Aug.  1,  19 — ,  interest  being  charged  on  overdue 
amounts  at  the  rate  of  6  %  ? 

393 


394 


PRACTICAL  BUSINESS  ARITHMETIC 


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Solution. 

Debits 

Date 

Tbrm  op 
Credit 

Maturity                 Item 

Interest 
Period 

Interest 

June  1 

30  da. 

July     1              $  900 

31  da. 

$4.65 

9 

10 

June  19                450 

43 

3.23 

20 

10 

30                300 
$1650 

Credits 

32 

1.60 

$9.48 

Date 

J                                     Interest 
*™**                                    Period 

Interest 

June  30 

$600                          32  da. 

$  3.20 

July  10 

300                           22 

1.10 

18 

150                           14 

$1050 

.35 
$4.65 

The  debit  footing  and  interest :  $  1650  +  $  0.48  =  $  1659.48 

The  credit  footing  and  interest:  $  1050  +  $4.65  =  %  1054.65 

The  balance  due  Aug.  1,  1907  =  $  604. 


WRITTEN    EXERCISE 

1.  Find  the  cash  balance  due  June  1,  19 — ,  on  problem  4, 
page  391,  money  being  worth  5%. 

2.  Equate  the  following  account  and  find  the  cash  balance 
due  Aug.  1,  19 — ,  money  being  worth  4J%. 

Frederick  T.  Lawrence 


ID- 

19— 

May 

4 

To  mdse.,  60  da. 

1360 

May 

14 

By  cash 

360 

17 

To  mdse.,  30  da. 

720 

June 

10 

By  cash 

300 

26 

To  mdse.,  60  da. 

1080 

21 

By  cash 

420 

To  find  the  cash  balance  of  an  equated  account :  Equate  the  account. 
Compute  the  interest  on  the  balance  of  the  account  from  the  equated  date  to  the 
date  of  settlement.  Add  the  interest  to  the  balance  of  the  account  and  the  result 
is  the  cash  balance  due. 


CASH  BALANCE 


395 


3-6.    The  following  is  a  page  from  a  sales  ledger.     Find  the 
cash  balance  due  on  each  account  Aug.  1,  money  being  worth  6  %. 


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DIVIDENDS   AND    INVESTMENTS 
CHAPTER   XXXIII 

STOCKS  AND    BONDS 
STOCKS 

469.  A  corporation,  or  stock  company,  is  an  association  of  indi- 
viduals organized  under  the  laws  of  a  particular  state  into  a 
body  which  is  by  law  given  the  rights  and  powers  and  civil 
liabilities  of  a  person. 

Being  a  mere  creature  of  law  a  corporation  possesses  only  those  proper- 
ties which  its  charter  (the  instrument  which  defines  its  rights  and  duties) 
confers  upon  it.  These  are  such  as  are  best  calculated  to  effect  the  object 
for  which  it  was  created.  Among  the  most  important  is  legal  continuous 
existence,  irrespective  of  that  of  the  individuals  composing  it. 

470.  The  capital  stock  of  a  corporation  represents  the  interest 
of  the  individuals  who  compose  the  corporate  body  m  the  prop- 
erty and  profits  of  the  corporation. 

The  capital  stock  is  divided  into  a  definite  number  of  shares.  It  is  not 
necessary  to  give  these  shares  a  par  value,'  but  it  is  customary  to  do  so. 
The  usual  par  value  of  a  share  is  SIOO.  However,  any  amount  may  be  the 
par  value. 

471.  A  stock  certificate  is  a  legal  instrument  which  evidences 
that  the  holder  owns  a  certain  number  of  shares  of  stock  in  the 
corporation  or  association  issuing  the  certificates.  A  stockholder 
is  a  person  who  owns  one  or  more  shares  of  stock. 

The  certificate  bears  the  seal  of  the  corporation  and  is  signed  by  officers 
(usually  the  president  and  the  treasurer  or  their  representatives)  authorized 
by  the  by-laws  to  sign  stock  certificates. 

Stockholders  elect  a  few  of  their  number  to  have  general  control  of  the 
company.  The  stockholders  thus  elected  constitute  the  board  of  directors. 
This  board  may  delegate  its  powers  to  several  of  its  members  called  an 
executive  committee.  The  control  of  a  corporation  is  vested  in  its  board 
pf  directors. 


STOCKS   AND    BONDS 


397 


472.  A  dividend  is  a  sum  of  money  paid  by  a  corporation  to 
its  stockholders,  each  share  participating  equally.  An  assess- 
ment is  an  amount  per  share  which  stockholders  are  called  upon 
to  pay  to  make  up  losses  or  deficiencies. 

The  board  of  directors  decide  upon  the  rate  of  dividend,  which  usually 
means  the  rate  j^er  annum  on  the  face  value  of  the  stock,  but  it  may  also  be 
expressed  as  a  certain  amount  in  dollars  and  cents  per  share. 

Shares  of  stock  may  be  non-assessable. 

473.  A  company  may  divide  its  stock  into  two  or  more  classes; 
the  usual  division  is  preferred  and  common. 


474.  Preferred  stock  is  stock  which  is  entitled,  out  of  profits, 
to  a  preferential  dividend  at  a  fixed  rate.  In  case  a  company 
is  dissolved,  its  preferred  stock  usually  has  a  preferential  claim 
against  the  assets  of  the  company  up  to  the  par  value  of  the 
preferred,  stock  outstanding. 

The  prior  rights  of  preferred  stocks  over  common  usually  make  them 
safer  investments,  but  stocks  are  not  necessarily  safe  because  preferred. 


398 


PEACTICAL   BUSINESS  ARITHMETIC 


475.  Common  Stock  is  the  stock  which  has  the  right  to  the 
equity  in  the  earnings  and  the  income  of  the  Uquidation  in  the 
assets  of  a  corporation  after  the  claims  of  all  prior  security  issues 
(bonds,  notes,  preferred  stock,  etc.)  have  been  satisfied. 


476.  The  par  value  is  the  face  value  of  stocks;  the  market 
value  is  the  sum  for  which  the  stocks  can  be  sold  in  the  market. 

477.  If  a  company  is  prosperous  and  pays  a  higher  rate  of 
dividend  than  the  money  could  earn  with  no  greater  risk  in  the 
general  money  market,  a  share  may  sell  for  more  than  its  face 
value  ;  it  is  then  said  to  be  above  par^  or  at  a  premium.  If  the  com- 
pany pays  a  lower  rate  of  dividend  than  could  be  obtained  at  no 
greater  risk  in  the  general  money  market,  a  share  may  sell  for 
less  than  its  face  value ;  it  is  then  helow  par^  or  at  a  discount. 

478.  A  stock  broker  is  a  person  who  buys  and  sells  stocks  for 
other  persons  on  commission. 

Stocks  are  usually  bought  and  sold  through  stock  brokers.  The  broker's 
commission  is  usually  |  %  of  the  par  value  of  the  stock,  or  Vl\  f  per  share. 
A  charge  is  made  for  either  buying  or  selling. 


STOCKS   AKD   BONDS  399 

479.  When  the  price  of  stock  is  quoted  at  97,  118|,  IBOJ, 
it  means  that  a  share  whose  par  value  is  SlOO  can  be  bought 
for  S97,  $118.75,  $160.50.  If  a  person  buys  stock  through  a 
broker  at  160|,  it  will  cost  him  $160.50  +  $0,121  brokerage,  or 
$160.62J  ;  if  he  sells  stock  through  a  broker  for  160|-,  he  will 
receive  as  proceeds  $160.50  -  $0,121,  or  $160.37|,  per  share. 

On  the  New  York  Stock  Exchange  quotations  are  expressed  in  dollars 
and  eighths  of  a  dollar. 

In  some  other  cities  quotations  are  expressed  in  dollars,  in  eighths  of  a 
dollar,  and  in  sixteenths  of  a  dollar.  When  stocks  are  quoted  at  less  than 
II  per  share,  fluctuations  are  sometimes  expressed  in  cents. 

The  bulk  of  transactions  in  the  stock  exchanges  is  in  round  lots.  In 
New  York  round  lots  are  100  shares  or  some  multiple  thereof ;  in  Boston, 
50  shares  or  some  multiple  thereof.  In  these  cities  any  other  number  of 
shares  than  the  ones  named  for  each  would  be  called  odd  lots.  In  Chicago 
no  distinction  is  made  between  round  and  odd  lots.  Fractional  shares  of 
stock  which  are  occasionally  in  the  market  are  called  scrip. 

ORAL    EXERCISE 

1.  Examine  the  certificate  of  stock,  page  397.  What  is  the 
name  of  the  company  ?  From  whom  did  the  company  get  its 
right  to  carry  on  business  as  a  corporation  ? 

2.  What  is  the  entire  capital  stock  of  the  company?  Into 
how  many  shares  is  this  divided  ?  What  per  cent  of  the  entire 
stock  of  the  company  does  the  holder  of  the  certificate  own  ? 

3.  What  kind  of  stock  is  represented  by  the  certificate  ? 
What  is  the  difference  between  common  and  preferred  stock  ? 

4.  What  is  the  par  value  of  each  share  ?  If  the  market  value 
of  each  share  is  $160,  what  is  the  certificate  worth  ? 

5.  What  sum  must  be  laid  aside  to  provide  for  the  dividends 
on  the  preferred  stock  of  the  company,  the  rate  being  6  %  ?  How 
much  of  this  sum  will  the  holder  of  the  certificate  receive  ? 

6.  Examine  the  stock  certificate,  page  398.  What  part  of 
the  stock  of  the  company  is  common  stock  ? 

7.  A  5  %  dividend  on  the  common  stock  would  require  how 
much  money  from  the  treasury  of  the  company  ?  Of  this  sum 
how  much  would  George  W.  Putnam  receive  ? 


400 


PRACTICAL   BUSINESS   ARITHMETIC 


Dividends  and  Assessments 
written  exercise 

Unless  otherwise  specified  the  par  value  of  a  share  will  be  understood  to 
be  1100. 

1.  A  company  with  83,500,000  capital  declares  an  8  %  divi- 
dend.     What  does  the  holder  of  250  shares  receive  ? 

2.  B  holds  450  shares  of  Lehigh  Valley  Railroad  stock. 
When  the  company  declares  a  dividend  7|^%,  how  much  will 
he  receive  ? 

3.  What  annual  income  is  derived  from  investing  $  48,000 
in  Union  Pacific  Railroad  stock  at  120,  if  2|  %  semiannual  divi- 
dends are  declared  ? 

4.  E.  H.  Rhodes  holds  600  shares  of  Lehigh  Valley  Railrpad 
stock.  If  lie  received  the  following  check  as  his  annual  divi- 
dend, what  was  the  rate  ? 


%jhe  %Tirst  >^ational  CXjank. 


Z=^S)oU€trs 


S>ioid4!nd  J{o.Jz^ 


feasurer 


5.  A  company  with  11,000,000  capital  declares  quarterly 
dividends  of  1^  % .  What  are  the  annual  dividends  ?  What  is 
the  amount  received  annually  by  D,  who  owns  475  shares  ? 

6.  A  corporation  with  a  capital  of  1 125,000  loses  $2500. 
What  per  cent  of  his  stock  must  each  stockholder  be  assessed 
to  meet  this  loss?  How  much  will  it  cost  A,  who  owns  150 
shares  ? 

7.  A  company  with  a  capital  of  %  750,000  declares  a  semi- 
annual dividend  of  3^%.  How  much  money  does  it  distribute 
among  its  stockholders  annually?  What  is  the  annual  income 
of  a  man  who  owns  200  shares  ? 


STOCKS   AND  BONDS  401 

8.  If  the  Pennsylvania  Railroad  declares  a  semiannual  divi- 
dend of  2i%  x)n  a  capital  stock  of  S  500,000,000,  what  amount 
is  annually  distributed  among  the  stockholders  ?  What  is  the 
annual  income  to  J.  P.  Morgan  from  this  stock  if  he  owns 
7,500,000  shares  having  a  par  value  of  1 50  each? 

9.  During  a  certain  year  a  manufacturing  concern  with 
a  capital  of  -i)  750,000  earns  •$  75,500  above  all  expenses.  It 
decides  to  save  §15,500  of  this  for  emergencies  and  to  divide 
the  remainder  in  dividends.  What  is  the  rate  ?  What  would 
be  the  amount  of  A's  dividend  check  if  he  owns  125  shares  ? 

10.  The  capital  stock  of  the  Gramercy  Finance  Company  is 
$1,500,000.  The  gross  earnings  of  the  company  for  a  year  are 
§375,000  and  the  expenses  1215,000.  What  even  per  cent  of 
dividend  may  be  declared  and  what  would  be  the  amount  of  un- 
divided profits  if  10%  of  the  net  earnings  are  first  set  aside  as  a 
surplus  fund  ?   (An  even  per  cent  is  a  per  cent  without  a  fraction.) 

11.  A  railway  company  has  a  capital  of  §3,500,000  and 
declares  dividends  semiannually.  During  the  period  from 
Jan.  1  to  July  1  of  a  certain  year  the  net  earnings  of  the  com- 
pany were  §191,000.  Of  this  amount  10  %  is  carried  to  surplus 
fund.  What  even  rate  per  cent  of  dividend  may  be  declared  on 
the  balance  and  how  much  will  be  carried  to  undivided  profits  ? 

12.  A  company  with  a  capital  stock  of  §500,000  gains  during 
a  certain  year  §38,750.  It  decides  to  carry  §5000  of  the 
profits  to  surplus  fund  and  to  declare  an  even  per  cent  of 
dividends  on  the  remainder.  What  sum  was  divided  among 
the  stockholders,  and  what  sum  was  carried  to  undivided 
profits  account  ?  What  was  the  annual  income  to  F  from  this 
stock  if  he  owned  500  shares  ? 

13.  During  a  certain  year  the  gross  earnings  of  a  railroad 
having  a  capital  stock  of  §100,000,000  were  §65,150,000,  and 
the  operating  expenses  §45,150,000.  If  the  company  declared 
a  semiannual  dividend  of  3^  %  and  carried  the  balance  of  the 
net  earnings  to  undivided  profits  account,  how  much  was 
divided  among  the  stockholders  ?  How  much  was  the  working 
capital  of  the  company  increased  ? 


402 


PRACTICAL  BUSINESS  ARITHMETIC 


14.  The  capital  stock  of  the  First  National  Bank  is  S  3,000,000, 
and  dividends  are  declared  semiannually.  The  profits  of  the 
bank  for  a  certain  six  months  are  $185,750.  Of  this  sum  10%  is 
carried  to  a  surplus  fund.  The  directors  then  vote  to  declare  a 
semiannual  dividend  of  3|^%  and  carry  the  balance  of  tlie  profits 
to  undivided  profits  account.  What  amount  was  carried  to  surplus 
fund  account?  to  dividend  account?  to  undivided  profits  account? 

Buying  and  Selling  Stock 
480.    The  following  is  an  abbreviated  form  of  the  stock  quo- 
tations for  a  certain  day  on  the  New  York  Stock  Exchange : 

Table  of  Sales  and  Range  of  Prices 


Sales 

Stocks 

Open. 

High. 

Low. 

Clos. 

Net  Change 

2,600 

Am.  Sugar .... 

lOOi 

lOOi 

99i 

99f 

-f 

200 

Am.  Sugar  (pfd.) 

110 

llOir 

109i 

109i 

-1 

10,200 

Atchison     .... 

95^ 

95i 

91f 

92 

-3i 

300 

Atchison  (pfd.)    .     . 

100 

100 

100 

.100 

900 

At.  Coast  Line     .     . 

121i 

120 

116 

116 

-4i 

13,600 

Baltimore  &  0.     .     . 

88i 

881 

87i 

88 

-i 

600 

Baltimore  &0.  (pfd.) 

80i 

81 

80i 

80i 

-i 

147,100 

Canadian  Pacific .     . 

1931 

200f 

188i 

1891 

-3f 

20,200 

Chic.  M.  &  St.  P.       . 

98| 

98+ 

94i 

95 

-3f 

300 

Chic.  M.&  St.  P.  (pfd.) 

137f 

135 

134^ 

134i 

-2 

200 

General  Chem.  (pfd.) 

108 

109 

108i 

109 

+  1 

2,500 

General  Electric  .     . 

144 

144 

141 

141 

-3 

15,600 

Gt.  Northern  (pfd.)  . 

122 

121f 

119 

119i 

-2i 

1,600 

Illinois  Central     .     . 

110 

110 

107i 

107f 

-2| 

59,800 

Lehigh  Valley      .     . 

136i 

136i 

132i 

134f 

-If 

650 

Louisville  &  Nash.     . 

135f 

135i 

131i 

131i 

-H 

2,100 

NatU  Biscuit    .     .     . 

131 

130i 

125 

125 

-5 

100 

Nat'l  Biscuit  (pfd.)  . 

123 

123i 

123f 

123^ 

+  i 

69,200 

South.  Pacific .     .     . 

92i 

9H 

86i 

87i 

-5i 

300 

South.  Pacific  (pfd.). 

lOOi 

97i 

97i 

97i 

-2f 

210,100 

Union  Pacific  .     .     . 

154i 

154i 

im 

1491 

-4 

400 

Union  Pacific  (pfd.)  . 

82i 

82i 

82 

82 

-i 

390,100 

U.S.  Steel  .... 

58i 

58f 

56 

56f 

-2| 

4,200 

U.S.  Steel  (pfd.)  .     . 

109 

109i 

107i 

107i 

-n 

In  the  first  column  is  shown  the  number  of  shares  of  stock  sold ;  in  the 
second,  the  name  of  the  stock ;  in  the  third,  fourth,  fifth,  and  sixth,  respec- 
tively, the  opening,  the  highest,  the  lowest,  and  the  closing  prices  of  the  day ; 
in  the  last,  the  net  changes  between  the  closing  price  of  yesterday  and  to-day. 
Thus,  2600  shares  of  American  Sugar  stock  were  sold.  The  opening  price 
was  1100.50  per  share  ;  the  highest  price  $  100.50  ;  the  lowest,  199.25  ;  the 
closing,  $99.75,  which  shows  a  decline  of  75)*  from  the  preceding  day. 


STOCKS  AND  BONDS  403 

ORAL    EXERCISE 

1.  Find  in  the  table  (page  402)  three  eases  where  a  quo- 
tation both  for  common  stock  and  for  preferred  (^})fd.  stands 
for  preferred)  stock  of  the  same  company  is  given.  Which  is 
worth  the  more  in  each  case  ?  The  par  value  of  all  shares  is 
SI  00. 

If  the  profits  of  a  concern  are  so  great  that  a  large  per  cent  may  be  paid 
on  the  common  stock,  after  paying  tlie  fixed  rate  on  the  preferred  stock, 
then  the  common  stock  may  sell  for  a  higher  figure  than  the  preferred. 

2.  What  would  100  shares  of  American  Sugar  (common)  cost 
if  bought  through  a  broker  at  the  lowest  price  for  the  day, 
brokerage  being  |-%. 

3.  What  would  the  seller  of  the  stock  realize  on  the  sale  ? 

Suggestion.  The  seller  would  receive  the  price  for  which  it  was  sold 
minus  the  brokerage,  \  %. 

4.  State  the  cost,  at  the  opening  price  in  the  table,  of  100 
shares  each  of  the  following  stocks,  assuming  that  the  transac- 
tions take  place  through  a  broker  who  charges  '^  %  commission : 
Baltimore  &  Ohio  ;  Canadian  Pacific  ;  General  Electric  ;  Lehigh 
Valley.     (Base  the  calculations  on  the  common  stock.) 

5.  At  the  highest  price  in  the  table,  state  the  amount  that 
would  be  received  from  the  sale  of  100  shares  of  each  of  the 
following  stocks,  assuming  that  they  were  sold  through  a  broker 
who  charged  |^'%  commission:  Southern  Pacific;  U.S.  Steel  (pre- 
ferred); Great  Northern  (preferred) ;  National  Biscuit;  Ameri- 
can Sugar  (preferred) ;  Atchison  ;  General  Chemical  (preferred) ; 
Illinois  Central ; .  Union  Pacific.  (If  preferred  is  not  named, 
common  stock  is  referred  to.) 

WRITTEN   EXERCISE 

Find  the  cost,  at  the  closing  price  in  the  table,  of  2500  shares  of 
the  following  stocks,  including  brokerage  : 

1.  Canadian  Pacific.  4.    Baltimore  &  Ohio  (pfd.). 

2.  American  Sugar  (pfd.).        5.    Atlantic  Coast  Line. 

3.  National  Biscuit  (pfd.).       6.    United  States  Steel  (pfd.). 


404  PRACTICAL   BUSINESS  ARITHMETIC 

At  the  closing  price  for  the  day  find  the  amount  received  from 
the  sale  of  3500  shares  of  the  following  stocks  sold  through  a  broker : 

7.  Illinois  Central.  il.    Atchison  (pfd.). 

8.  Louisville  &  Nashville.  12.    General  Electric. 

9.  Southern  Pacific.  13.    Southern  Pacific  (pfd.). 
10.    Lehigh  Valley.  14.    Great  Northern  (pfd.). 

481.  Example.  I  bought  1000  shares  Chicago,  Milwaukee,  & 
St.  Paul  preferred  stock,  at  the  lowest  price  in  the  table,  and 
sold  the  same  at  1401.    Allowing  for  brokerage  both  for  buying 

and  selling',  did  I  gain  or  lose,  and  how  much  ? 

S140  371 
Solution.     Since  I  bought  through  a  broker,  each  share  *       2 

cost  me  $  134.871  +  |0.12^,  or  $  135  ;  and  since  I  sold  through  1^5.00 

a  broker,  the  proceeds  of  each  share  sold  was  $140.50  —  .^0.12^,  S  5.37i- 

or  $140.37|.     $  140.371  -  $135.00  :=  S5.37|,   gain   on   each  1000 

share.     Since  1 5.37^  is  gained  on  each  share,  1000  times  

|5.37i,  or  $5375,  is  gained  on  1000  shares.  ^bdlb. 

In  the  following  exercise  it  is  understood  that  all  sales  and  purchases  are 
made  through  a  broker,  who  charges  a  commission  of  i%  both  for  buying 
and  for  selling. 

WRITTEN    EXERCISE 

Find  the  gain  or  loss  on  500  shares  of  each  of  the  following  stocks 
bought  at  the  opening  price  and  sold  at  the  price  here  given : 

1.  Illinois  Central,  108|.  5.  American  Sugar  (pfd.),  103. 

2.  General  Electric,  147|.  6.  National  Biscuit,  134i. 

3.  Southern  Pacific  (pfd.),  89.  7.  Baltimore  &  Ohio,  90|. 

4.  General  Chemical  (pfd.),  110.  8.  Canadian  Pacific,  200^. 

9.  United  States  Steel  (pfd.),  112 1. 

10.  Atlantic  Coast  Line,  115|. 

11.  Great  Northern  (pfd.),  125. 

12.  National  Biscuit  (pfd.),  126|. 

13-24.  Find  the  gain  or  the  loss  on  1000  shares  of  each  of 
the  above  stocks  bought  at  the  lowest  price  and  sold  at  the 
highest  price,  in  the  table. 

25.  John  R.  West  bought  400  shares  of  United  States  Steel, 
(common)  at  the  opening  price  in  the  table  and  sold  it  so  as  to 
gain  $300.     What  was  the  quoted  price  when  he  sold  it? 


STOCKS   AND   BONDS  405 

26.  I  bought  some  United  States  Steel  (preferred)  at  the 
opening  price  in  the  table  and  sold  it  for  112i.  If  I  gained 
S650  by  the  transaction,  how  many  shares  did  I  buy? 

27.  I  bought  2500  shares  of  General  Electric  at  the  lowest 
price  in  the  table,  held  it  for  a  year,  received  5  %  in  dividends, 
and  then  sold  it  at  139|.  If  money  was  worth  41  %,  did  I  gain 
or  lose,  and  how  much  ? 

The  interest  is  to  be  computed  on  the  cost  of  the  stock,  the  dividend  on 
the  par  value. 

28.  I  gave  my  broker  orders  to  buy  1500  shares  of  Atchison 
(preferred)  and  to  sell  2000  shares  of  Canadian  Pacific.  If  he 
bought  at  the  lowest  price  in  the  table  and  sold  at  the  highest 
price,  what  balance  will  he  put  to  my  credit  ? 

BONDS 

482.  A  bond  is  an  instrument  by  which  a  government,  a 
municipality,  or  a  corporation  contracts  and  agrees  to  pay  a 
specified  sum  of  money  on  a  given  date,  at  a  specified  rate  of 
interest.  —  Rollins. 

Bonds  are  generally  issued  at  a  face  value  of  $  1000 ;  less  frequently,  of 
•$500  ;  occasionally,  of  f  100.  All  bonds  of  the  same  issue  usually  have  the 
same  rights  and  security. 

Bonds,  the  payment  of  which  depends  only  on  the  unsecured  credit  of 
the  issuing  company,  are  called  debenture  bonds;  those  that  have  their  pay- 
ment secured  by  a  mortgage  on  the  property  of  the  issuing  corporation 
are  called  mortgage  bonds  ;  those  that  are  secured  by  a  deposit  with  a  trustee 
of  collateral  are  called  collateral  trust  bonds ;  those  that  provide  that  the 
interest  on  them  shall  be  paid  only  if  earned  are  called  income  bonds. 

Bonds  of  a  national  govermnent  are  called  government  bonds;  of  a  state, 
a  city,  a  town,  or  other  municipal  organization,  municipal  bonds. 

The  names  of  the  different  government  bonds  are  usually  derived  from 
the  interest  they  bear  and  the  time  when  they  mature.  Thus,  "  U.  S.  2s, 
1930,"  are  United  States  bonds  bearing  interest  at  2%  and  maturing  in  1930. 

From  the  gross  earnings  of  a  company  the  operating  expenses  are  first 
deducted;  from  the  net  earnings  are  deducted  all  fixed  charges,  such  as 
interest  on  bonds ;  then  the  dividends  on  preferred  stock  are  paid ;  and 
finally  out  of  the  remainder  dividends  on  the  common  stock  are  paid. 


406  PRACTICAL   BUSINESS  ARITHMETIC 

483.  With  reference  to  the  form  of  contract  for  the  payment 
of  principal  and  interest  there  are  two  kinds  of  bonds :  coupon 
and  registered. 


484.  A  coupon  bond  is  a  bond  to  which  are  attached  interest 
notes,  or  coupons,  representing  the  interest  due  on  the  bond  at 
stated  periods  of  payment. 


STOCKIS   AND   BONDS  407 

The  interest  notes  may  be  cut  off  from  the  bonds  at  maturity  and  the 
amount  of  interest  which  they  represent  collected  through  a  bank.  If  these 
notes  are  not  paid  when  due,  they  bear  interest  at  the  legal  rate. 

485.  A  registered  bond  is  a  bond  which  has  no  separate  con- 
tract for  the  payment  of  the  interest.  Such  a  bond  must  be 
recorded  on  the  books  of  the  corporation  in  the  name  of  the 
holder  to  whom  the  mterest  is  sent  by  check. 

Coupon  bonds  may  be  made  j>ayable  either  to  bearer  or  registered  as  to 
principal  only  (the  first  custom  prevails  generally),  and  may  be  transferred 
by  delivery  or  indorsement  accordingly.  Registered  bonds  are  always 
drawn  payable  to  some  designated  person  and  can  be  transferred  only  by 
assignment  and  registry  on  the  books  of  the  corporation. 

ORAL   EXERCISE 

1.  Examine  the  bond  on  page  406.  With  reference  to  tlie 
form  of  contract,  what  kind  of  a  bond  is  it  ? 

2.  How  many  interest  notes  (coupons)  Avould  be  attached  to 
the  full  bond? 

3.  When  was  the  bond  issued  ?  What  date  (of  maturity) 
should  be  written  on  each  interest  note  ? 

4.  What  is  the  face  of  the  bond  ?  What  rate  of  interest  does 
it  bear  ?     What  sum  should  be  written  on  each  interest  note  ? 

5.  How  may  coupon  bonds  be  transferred  ?  registered  bonds  ? 

All  bonds  are  bought  and  sold  "  and  interest  " ;  that  is,  interest  should  be 
reckoned  on  the  par  value  from  the  date  of  the  last  interest  payment  to  the 
date  of  the  purchase  or  sale,  at  the  rate  which  the  bond  pays. 

6.  If  the  bond  on  page  406  was  quoted  at  105|^  when  it  was 
purchased,  how  much  did  it  cost,  including  1  %  brokerage  ? 
How  much  did  the  seller  realize  on  it,  if  sold  Aug.  1.  1915  ? 

7.  Has  the  city  or  town  in  which  you  live  any  bonded  in- 
debtedness (mdebtedness  secured  by  bonds)  ?  If  so,  what  are 
these  bonds  called,  and  what  rate  of  interest  do  they  pay  ? 

8.  What  is  the  difference  in  the  meaning  of  government  bond 
and  municipal  bond  ?  Upon  what  authority  does  the  government 
issue  bonds  ?  Upon  what  authority  does  a  town  or  a  city  issue 
bonds  ?  Must  the  bond  issue  be  approved  by  the  state  in  which 
the  town  or  the  city  is  located  ? 


408  PEACTICAL  BUSINESS  ARITHMETIC 

The  Use  of  Bond  Tables 

486.  The  use  of  tables  for  finding  tlie  interest  on  notes, 
bonds,  etc.,  is  common  among  bankers  and  brokers.  No  interest 
tables  are  illustrated  in  this  connection  because  they  are  too 
extended  and  complex  for  a  textbook. 

Referring  to  the  bond  table,  page  409,  the  per  cents  at  the  top  of 
the  table  represent  the  income  on  the  face  of  a  bond  at  one  of 
the  given  rates,  and  the  per  cents  given  in  the  column  at  the  left 
represent  the  income  that  will  be  realized  when  a  bond  is  bought 
at  a  certain  market  price.  This  table  is  for  a  bond  maturing  20 
yr.  from  date,  with  interest  payable  semiannually. 

487.  Example.  What  will  be  the  net  income  on  a  5  %  bond 
bought  at  97.53? 

Solution.  In  the  column  headed  5%  find  the  price  named,  97.53,  then  fol- 
low this  line  to  the  left  and  note  that  in  the  Ter  Cent  per  Annum  column  6.20 
is  given;  the  net  income  on  the  price  paid  for  the  bond,  97.53,  will  be  5.2%. 

ORAL    EXERCISE 

He/er  to  the  table  and  find  the  cost  of: 

1.  A  6  %  bond  that  will  net  61  %. 

2.  A  3  %  bond  that  will  net  5  %. 

3.  A  41  %  bond  that  will  net  4.8  %. 

4.  A  4  %,  bond  that  will  net  51  %. 

5.  A  man  purchased  4  bonds,  as  follows :  a  3  %  bond  that 
would  net  4.6  %  ;  a  41  %  bond  that  would  net  4:%;  a  5  %  bond 
that  would  net  41  %.     What  did  he  pay  for  each  bond  ? 

Refer  to  the  table  and  find  the  net  income  of  : 

6.  A  5  %  bond  that  will  cost  $91.15. 

7.  A  7%  bond  that  will  cost  S125.10. 

8.  A  3%  bond  that  will  cost  S 79.95. 

9.  A  6  %  bond  that  will  cost  S  106.02. 

10.  A  man  purchased  5  bonds  each  of  which  netted  him  5  % 
income.  If  the  bonds  which  he  bought  yielded,  on  the  face 
value,  the  following  rate  of  income,  what  did  he  pay  for  each 
one :  4  %,  31  %,  5  %,  6  %,  and  7  %  ? 


STOCKS  AND   BONDS 


409 


A  BOND   TABLE 

20-YEAR.    Interest  Payable  semiannually 


Per  Cent 
PER  Annum 

3% 

^% 

4% 

H% 

5% 

6% 

7% 

3.70 

90.17 

97.19 

104.21 

111.24 

118.26 

132.30 

146.35 

31 

89.51 

96.50 

103.50 

110.49 

117.48 

131.46 

145.44 

3.80 

88.80 

95.82 

102.78 

109.74 

116.70 

130.63 

144.55 

H 

87.90 

94.81 

101.73 

108.64 

115.56 

129.39 

143.22 

3.90 

87.58 

94.48 

101.38 

108.28 

115.18 

128.98 

142.78 

4. 

80.32 

93.16 

100.00 

106.84 

113.68 

127.36 

141.03 

4.10 

85.09 

91.86 

98.64 

105.42 

112.20 

125.76 

139.32 

4i 

84.78 

91.54 

98.31 

105.07 

111.84 

125.37 

138.90 

4.20 

83.87 

90.59 

97.31 

104.03 

110.75 

124.19 

137.63 

H 

83.27 

89.96 

96.65 

103.35 

110.04 

123.42 

136.80 

4.30 

82.68 

89.34 

96.00 

102.66 

109.33 

122.65 

135.98 

4f 

81.80 

88.42 

95.04 

101.65 

108.27 

121.51 

134.75 

4.40 

81.51 

88.11 

94.72 

101.32 

107.93 

121.14 

134.35 

H 

80.35 

86.90 

93.45 

100.00 

106.55 

119.65 

132.74 

4.00 

79.22 

85.72 

92.21 

98.70 

105.19 

118.18 

131.16 

H 

78.94 

85.42 

91.90 

98.38 

104.86 

117.82 

130.77 

4.70 

78.11 

84.55 

90.99 

97.43 

103.86 

116.74 

129.61 

4f 

77.57 

83.98 

90.39 

96.80 

103.20 

116.02 

128.84 

4.80 

77.02 

83.40 

89.79 

96.17 

102.55 

115.32 

128.08 

4| 

76.22 

82.56 

88.90 

95.24 

101.59 

114.27 

126.95 

4.90 

75.95 

82.28 

88.61 

94.94 

J01.27 

113.92 

126.58 

5. 

74.90 

81.17 

87.45 

93.72 

100.00 

112.55 

125.10 

5.10 

73.86 

80.09 

86.31 

92.53 

98.76 

111.20 

123.65 

5i 

73.61 

79.82 

86.03 

92.24 

98.45 

110.87 

123.29 

5.20 

72.85 

79.02 

85.19 

91.36 

97.53 

109.87 

122.22 

5i         . 

72.34 

78.49 

84.64 

90.78 

96.93 

109.22 

121.51 

5.30 

71.85 

77.97 

84.09 

90.21 

96.33 

108.57 

120.81 

5f 

71.11 

77.19 

83.27 

89.36 

95.44 

107.60 

119.77 

5.40 

70.87 

76.94 

83.01 

89.07 

95.14 

107.28 

119.42 

H 

69.90 

75.92 

81.94 

87.96 

93.98 

106.02 

118.06 

51 

68.72 

74.68 

80.64 

86.59 

92.55 

104.47 

116.38 

5f 

67.57 

73.46 

79.36 

85.26 

91.15 

102.95 

114.74 

51 

66.43 

72.27 

78.11 

83.95 

89.78 

101.46 

113.13 

6. 

65.33 

71.11 

76.89 

82.66 

88.44 

100.00 

111.56 

6i 

64.25 

69.97 

75.69 

81.41 

87.13 

98.57 

110.01 

Qi 

63.19 

68.85 

74.51 

80.18 

85.84 

97.17 

108.50 

6| 

62.15 

67.76 

73.36 

78.07 

84.58 

95.79 

107.01 

6^ 

61.14 

66.69 

72.24 

77.79 

83.34 

94.45 

105.55 

6f 

60.14 

65.64 

71.14 

76.64 

82.13 

93.13 

104.12 

61 

59.17 

64.62 

70.06 

75.50 

80.95 

91.83 

102.72 

6i 

58.22 

63.61 

69.00 

74.39 

79.78 

90.57 

101.35 

7. 

57.29 

62.63 

67.97 

73.31 

78.64 

89.32 

100.00 

410 


PRACTICAL  BUSINESS  ARITHMETIC 


Buying  and  Selling  Bonds 

488.  Bonds  are  generally  bought  and  sold  through  invest- 
ment bankers  or  private  bankers. 

Tlie  commission  for  buying  and  selling  bonds  is  the  same  as 
for  buying  and  selling  stocks. 

489.  The  following  table  is  an  abbreviated  form  of  the  sales, 
and  the  opening,  highest,  lowest,  and  closing  prices  of  bonds 
traded  in  on  the  New  York  Exchange  on  a  recent  date. 

Table  of  Sales  and  Range  of  Prices 


Sales 

Bonds 

Open, 

High. 

Low. 

Clos. 

Net  Chance 

5,000 

Am.  Hide  &  Leather 

6s 

103i 

103i 

103 

104 

+  f 

8,000 

Brooklyn  Rapid  Tran- 

sit con. 5s .     .     .     . 

103 

103 

102f 

103 

6,000 

Chesapeake  &  Ohio  5s 

1061 

107i 

1061 

107i 

+  f 

81,000 

Chicago,  Burlington  & 

Quincy  4s      .     .     . 

93i 

93i 

92f 

92f 

-  1 

15,000 

Erie  1st  con.  4s     .     . 

851 

85f 

85 

85 

-1 

1,000 

Illinois  Central  4s  .     . 

93i 

93i 

93i 

93^ 

11,000 

Lehigh  Valley  con.  4^s 

99f 

m 

991 

m 

-i 

1,000 

Louisville  &  Nashville 

gold  5s      .... 

108 

110 

110 

110 

+  2 

2,000 

Manhattan  Ry.con.4s 

92 

92i 

91| 

m 

-i 

8,000 

Missouri  Pacific  4s     . 

59 

57 

56 

56 

-2 

24,000 

N.Y.  Central  &  Hud- 

son River  4s  1934  . 

m 

911 

89i 

90 

•  -  H 

35,000 

Reading  general  4s    . 

m 

95 

94i 

9H 

-i 

1,000 

Standard  Gas  6s    .     . 

m 

89f 

89f 

89 

-f 

4,000 

Texas  Pacific  1st  5s  . 

102 

102i 

102 

lOU 

-1 

62,000 

Union  Pacific  1st  4s  . 

m 

m 

97i 

9()| 

-f 

196,000 

United  Steel  5s      .     . 

102ir 

1021 

102i 

10l| 

-i 

18,000 

Wabash  1st  5s  .     .     . 

103^ 

104 

103i 

102f 

-1 

8,000 

West  Shore  4s  .     . 

93i 

94 

93f 

93i 

-i 

In  the  first  column  is  shown  the  par  value  of  the  bonds  sold;  in  the 
second,  the  name  of  the  bonds  and  the  interest  they  bear ;  in  the  third, 
fourth,  fifth,  and  sixth,  respectively,  the  opening,  highest,  low^est,  and 
closing  prices  of  the  day.  In  the  last  column,  Net  Cliamje,  the  net  changes 
between  the  closing  prices  of  the  given  day  and  the  closing  prices  of  the 
day  preceding.  Thus,  on  the  day  given,  $8000  worth  of  Brooklyn  Rapid 
Transit  bonds  bearing  5  %  interest  were  sold.  The  opening  price  was  $  103 
per  $100  of  par  value ;  the  highest  price,  $103  ;  the  lowest  price,  $102.621 ; 
the  closing  price,  $  103  ;  there  was  no  change  between  the  closing  price  of 
the  day  given  and  the  day  preceding. 


STOCKS   AND   BONDS  411 

490.  Example.  What  is  the  cost  of  $50,000  (par  vakie) 
Chicago,  Burlington  &  Quincy  4%  bonds  at  the  highest  price 
quoted  in  the  table  (page  410)  ? 

Solution.    $100  of  par  value  cost  ifiOSf  +  .$0.12|  brokerage,  or  $<H. 

.-.  $50,000  of  par  value  will  cost  500,  i.e.,  ($50,000 -^$  100)  times  $94,  or $47,000. 

WRITTEN   EXERCISE 

(Omit  the  interest  in  solving  these  problems) 

1.  What  is  the  cost  of  S  25,000  American  Hide  and  Leather 
bonds  at  the  opening  price  in  the  table  ? 

2.  I  gave  my  broker  orders  to  sell  S  10,000  Chesapeake  & 
Ohio  5  %  bonds  and  buy  $10,000  Texas  Pacific  1st  5  %  bonds. 
If  he  sold  at  the  highest  price  m  the  table  and  bought  at  the 
lowest  price,  what  balance  should  he  place  to  my  credit  ? 

3.  Find  the  proceeds  from  these  sales :  $1000  United  Steel  5  % 
bonds  at  the  opening  price  in  the  table ;  $  5000  Illinois  Central 
4  %  bonds  at  the  opening  price  in  the  table ;  $  75,000  Chicago, 
Burlington  &  Quincy  4  %  bonds  at  the  closing  price  in  the  table ; 
$10,000  Erie  4%  bonds  at  the  lowest  price  in  the  table. 

4.  June  1, 1915,  a  certam  city  borrowed  $  250,000  with  which 
to  build  a  new  high  school,  and  issued  41  %  10-yr.  coupon  bonds 
as  security.  If  these  bonds  sold  (through  a  broker)  at  101 1, 
how  much  was  received  by  the  city?  If  A  bought  five  $1000 
bonds,  how  much  did  they  cost  him?  If  interest  is  payable 
semiannually,  what  date  (of  maturity)  should  the  last  interest 
note  of  each  bond  bear  ?  What  will  be  the  amount  of  each 
uiterest  note  ? 

5.  Find  the  total  cost  of  the  following  purchases:  $20,000 
Erie  4%  bonds  at  the  closing  price  in  the  table;  $2000  Illinois 
Central  4  %  bonds  at  the  lowest  price  in  the  table ;  $5000  Louis- 
ville &  Nashville  5%  bonds  at  the  lowest  price  in  the  table; 
$15,000  Missouri  Pacific  4  %  bonds  at  the  opening  price  in  the 
table;  $10,000  Manhattan  Railway  4  %  bonds  at  the  lowest  price 
in  the  table;  $3000  West  Shore  4  %  Ixnids  at  the  opening  price 
in  the  table. 


412  PRACTICAL   BUSINESS   ARITHMETIC 

INCOMES   AND   INVESTMENTS 

491.  The  income  received  on  bonds  involves  the  consideration 
of  the  income  on  the  face  of  the  bond  in  comparison  with  the 
income  on  the  price  paid  for  the  bond.  To  illustrate :  if  a  6  % 
bond  is  bought  at  120,  the  annual  income  is  S6,  but  the  rate  of 
income  on  the  price  paid  for  the  bond  is  5  %,  brokerage  omitted. 
From  this  statement  it  is  clear  that  the  investor  would  receive 
5  %  on  his  investment,  but  it  must  be  remembered  that  at  the 
maturity  of  the  bond,  say  5  yr.,  he  will  receive  only  SI 00  for 
it ;  hence  he  must  deduct  the  difference  between  the  face  of  the 
bond  and  the  price  paid  for  it,  S  20,  to  get  the  net  sum  received 
as  income.  It  is  clear  that  the  investor  will  not  realize  5  %  on 
his  investment. 

The  above  statement  suggests  a  complex  problem  that  is  fully 
worked  out  in  bond  tables,  but  these  are  too  extended  to  be 
used  in  a  textbook.  This  question  is  referred  to  in  this  text  as 
a  caution  to  those  who  buy  bonds  regarding  the  net  income  they 
will  receive  on  the  sum  paid  for  the  bond.  It  is  easy  for  one  to 
deceive  himself  on  this  point. 

The  following  is  from  "Money  and  Investments,"  by  Mont- 
gomery Rollins,  to  whom  the  author  is  indebted  for  the  bond 
table  used  on  page  409. 

Take  as  an  example  a  bond  bearing  5  %  interest,  and  hav- 
ing exactly  10  yr.  to  run  before  maturity.  If  it  is  sold  at 
S  108.18,  that  is,  S  1081.80  for  each  one-thousand-dollar  bond, 
the  net  return  to  the  investor  would  be  4  %  per  annum,  which 
is  4  %  for  each  of  the  10  yr.,  and  is  4  %  upon  the  entire'  sum, 
S  1081.80,  invested. 

This  brings  up  the  point  that,  although  in  the  example,  the 
bond  costs  S  1081.80,  at  the  end  of  10  yr.,  when  it  matures, 
the  holder  will  receive  SIOOO.  In  the  meantime  he  will 
have  received  S50  yearly  in  interest.  Not  all  of  this  S50 
should  be  considered  as  income,  for  a  sufficient  amount  of  it 
should  be  set  aside  each  year  to  liquidate  the  $81.80  premium 
paid  for  the  bond. 


STOCKS  AND  BONDS  413 

COST  OF  BONDS 

492.  A  purchaser  of  a  bond  pays  the  market  price  of  the  bond 
plus  the  interest  accrued  since  the  last  interest  day.  In  finding 
the  cost  of  bonds  April  1  and  October  1  will  be  considered  as 
the  interest  days,  mterest  being  paid  semiannually.  If  a  bond 
were  purchased  after  any  one  of  these  dates,  the  buyer  would 
pay  the  market  price  of  the  bond  plus  the  interest  from  the 
last  interest  day  to  the  date  of  purchase.  Each  bond  is  of  a 
denomination  of  SIOOO. 

In  all  stock-exchange  transactions  in  bonds  a  commission  (brokerage) 
is  added  or  deducted  in  sales  or  purchases,  but  when  bonds  are  bought 
from  a  regular  bond  house,  the  price  quoted  is  net,  i.e.,  no  commission  is 
to  be  added. 

The  examples  in  the  text  are  stock-exchange  transactions. 

In  these  examples  compute  the  interest  for  the  exact  number  of  days. 

493.  Example.  What  will  be  the  cost  of  10  Western  Electric 
5%  bonds  at  102|,  with  brokerage  added,  if  purchased  on  May  1  ? 

Solution.    1  bond  costs  $1023.75,  without  interest. 

10  bonds  will  cost  $  10,237.50,  without  interest. 

April  1  to  May  1  is  1  mo. 

Interest  on  $10,000  for  1  mo.  at  5%  =  $41.67. 

$10,237.50  +  $41.67  =  $10,279.17,  cost  plus  the  interest. 

Brokerage,  |%  =  $12.50. 

$10,279.17  -I-  $12.50  =  $10,291.67,  total  cost. 

WRITTEN   EXERCISE 

Find  the  total  cost,  including  brokerage,  of  the  following : 

1.  10  Third  Avenue  1st  5s  at  107^,  bought  on  June  1. 

2.  20  Union  Pacific  1st  4s  at  98,  bought  on  July  16. 

3.  5  Southern  Railway  general  4s  at  76,  bought  on  July  21. 

4.  15  West  Shore  4s  at  931,  bought  on  July  31. 

5.  8  Western  Maryland  4s  at  791,  bought  on  Oct.  1. 

6.  12  U.  S.  Rubber  6s  at  103|,  bought  on  Oct.  31. 

7.  6  National  Tube  5s  at  99|,  bought  on  Nov.  1. 

8.  10  N.  Y.  Telephone  4ls  at  97J,  bought  on  Dec.  1. 

9.  10  Oregon  Short  Line  6s  at  110|,  bought  on  Jan.  30. 


414 


PRACTICAL  BUSINESS  ARITHMETIC 


STOCK   EXCHANGES 

494.  A  stock  exchange  is  an  association  of  brokers  for  the 
purpose  of  provicUng  a  common  meeting  place,  convenience,  and 
security  for  their  dealings  with  each  other.  The  principal  stock 
market  of  the  United  States  is  the  New  York  Stock  Exchange, 
an  unincorporated  association  of  1100  members. 

There  are  also  stock  exchanges  in  some  of  the  other  principal  cities.  Next 
in  importance  to  the  New  York  Stock  Exchange  are  the  stock  exchanges 

of  Boston,  Philadelphia,  and 


Interior  of  a  Stock  Exchange 


Chicago.  Many  stocks  of  large 
issue  are  dealt  in  on  several 
stock  exchanges.  Each  ex- 
change, as  a  rule,  forms  the 
principal  market  for  the  stocks 
which  are  controlled  by  local 
interests.  Stock  exchanges 
make  public,  as  they  occur,  the 
record  of  sales  and  quotations 
of  the  securities  in  which  the 
exchange  elects  to  deal.  In 
this  way  a  holder  of  securities 
which  are  dealt  in,  or  listed,  on 
an  exchange  may  know  the 
most  recent,  price  at  which  his  securities  have  sold  in  the  market,  and  an 
intending  investor  may  know  what  he  may  have  to  pay  for  such  securities. 
A  membership  in  a  stock  exchange  is  called  a  seat.  The  price  of  a 
seat  varies  from  .^1000  to  $20,000  on  local  stock  exchanges,  to  from  $30,000 
to  $75,000  on  the  New  York  Stock  Exchange.  A  stock  exchange  always 
maintains  a  uniform  rate  of  commission.  This,  as  has  been  seen,  is  usually 
1%,  or  $12.50  per  100  shares. 

The  importance  of  the  stock  exchange  is  shown  in  the  initial  financial 
results  of  the  great  European  war  which  began  in  1914.  When  hostilities 
were  imminent  the  stock  exchanges  of  the  leading  cities  of  Europe  and 
America  were  closed.  By  this  means  reckless  financial  transactions  were 
rendered  much  more  difficult,  because  it  made  quite  impossible  such  heavy 
sales  of  stocks  and  bonds  as  would  have  demoralized  the  money  market 
and  imposed  a  great  hardship  and  loss  on  holders  of  securities,  especially 
small  holders,  ^yhile  the  stock  exchanges  were  closed  the  sale  of  listed 
securities  was  rendered  difficult  l>ecause  of  the  lack  of  a  common  center 
for  sellinsf  such  vSecurities. 


STOCKS  AND  BONDS 


415 


495.  The  principal  ways  in  which  stocks  are  bought  and  sold 
are  as  follows :  stocks  bought  or  sold  are  deliverable  on  the  fol- 
lowing day  unless  otherwise  specified ;  this  is  called  "  regular  " 
delivery.  However,  securities  are  not  delivered  on  Saturdays  nor 
on  stock  exchange  holidays.  Transactions  may  be  for  "  cash," 
that  is,  deliverable  on  the  day  of  sale  ;  "  at  3  da.,"  that  is,  deliver- 
able on  the  third  day  following  the  sale ;  "buyer's  option,"  that  is, 
deliverable  at  the  option  of  the  buyer  at  any  time  within  the  option 
period  (from  4  to  60  da.)  ;  "seller's  option,"  that  is,  deliverable  at 
the  option  of  the  seller  at  any  time  within  the  option  period. 

By  far  the  largest  part  of  the  sales  are  "regular,"  On  "cash,"  "regular," 
and  "  at  3  da."  sales  no  interest  is  paid ;  but  on  options  over  3  da.,  interest 
at  the  legal  rate  on  the  selling  price  of  the  stock  is  paid  by  the  buyer  to  the 
seller.     To  terminate  an  option  of  over  3  da.,  one  day's  notice  is  required. 

496.  A  margin  is  a  sum  of  money  deposited  with  a  broker  to 
cover  losses  which  he  may  sustain  on  behalf  of  his  principal. 

Stocks  and  bonds  are  often  bought  and  sold  on  a  margin,  as  follows : 
June  8,  A.  M.  Grey  son  deposited  with  Richard  Roe  &  Co.,  his  brokers, 
$  4160,  and  instructed  them  to  buy  400  shares  of  Atchison,  Topeka  and  Santa 
Fe  Railroad  stock  whenever  they  could  do  so  at  104.  On  the  same  day  the 
stock  was  bought  in  accordance  with  instructions.  On  June  14,  pursuant 
to  instructions,  Richard  Roe  &  Co.  sold  the  stock  at  107 J  and  sent  A.  M. 
Greyson  the  following  statement  and  a  check  for  $5322.56. 


M^^ 


^7^^ 


New  York, 


■e-i'.^L>,4-r?'?7^ 


'^^^y?  j>^  /  e/:^ 


.19- 


/^^ 


-/yy'^Jl-^'M<~^^^ 


In  account  current  with  RICHARD  ROE  &  CO. 

DATE 

AMOUNT 

DAYS 

INTEREST 

DATE 

AMOUNT 

DAYS 

INTEREST 

A- 

7^ '/^DO-dA^a.^u^ 

oe 

OO 

c 

^/ 

Co 

^U^ 

r 

/4^ 

1^  c^rvteyU..ay/^ 

OO 
OO 

C 

^7 

i^yoio 

OO 

*/■/ 

Co 

¥7oCo 

OO 

4^/ 

Co 

M 

H 

H 

H 

By  the  above  transactions  A.  M.  Greyson  has  gained  $1162.56. 

The  amount  of  margins  demanded  by  a  broker  depends  upon  the  charac- 
ter of  the  stocks  traded  in.  On  stocks  that  have  a  good  market  10%  of  the 
market  value  is  usually  demanded ;  on  stocks  that  have  little  or  no  market 


416  PRACTICAL   BUSINESS   ARITHMETIC 

20  %  of  the  market  value  or  more  is  often  required.  The  broker,  of  course, 
pays  for  the  stock  in  full.  In  order  to  do  this  he  is  frequently  obliged 
to  borrow  money  from  a  bank.  This  he  may  usually  do  by  depositing 
(hypothecating)  stock  as  security  (see  page  335). 

The  speculators  on  the  stock  exchange  may  be  divided  into  two  classes : 
bulls  and  be^rs.  A  bull  is  a  speculator  who  buys  stocks  in  the  expectation 
of  selling  them  at  a  higher  price.  A  bear  is  a  speculator  who  sells  stocks 
which  he  does  not  own,  in  the  expectation  that  he  can  buy  them  at  a  lower 
price  before  the  date  on  which  they  must  be  delivered.  A  bull  who  has 
bought  is  said  to  be  long  of  stock  ;  a  bear  who  has  sold  is  said  to  have  sold 
sliort,  or  to  be  slwrt  of  stock.  A  bull  works  for  advancing  prices ;  a  bear 
for  declining  prices.  A  bull,  when  selling  at  higher  prices,  is  said  to  have 
realized  his  profits,  or  to  have  liquidated  if  he  sells,  whether  the  price  he 
received  is  higher  or  lower  than  the  price  he  paid.  The  term  liquidate 
signifies  the  selling  of  securities  held  for  long  account  and  implies  no  dis- 
tinction between  sales  at  a  profit  or  sales  at  a  loss.  A  bear,  when  he  buys 
stock,  is  said  to  have  covered,  no  matter  whether  he  bought  at  a  gain  or 
at  a  loss. 

WRITTEN    EXERCISE 

(All  interest  computations  are  at  6%) 

1.  On  June  25  I  purchased,  through  a  broker,  300  shares 
of  Amalgamated  Copper  at  67|-  b.  3  (buyer's  option  any  time 
within  3  da.).  On  June  28  the  stock  was  dehvered  and,  pur- 
suant to  my  instructions,  sold  for  69|  cash.  Did  I  gain  or  lose, 
and  how  much  ? 

2.  On  April  15  my  broker  purchased  for  me  500  shares 
Delaware  &  Hudson  at  1721  regular.  On  April  16  he  sold  the 
same  at  174|  cash.     What  was  my  gain  ? 

3.  On  Sept.  15  I  bought,  through  a  broker,  250  shares  Read- 
ing (preferred)  at  68|  b.  30.  On  Sept.  25  my  broker  demanded 
the  stock  and,  in  accordance  with  my  instructions,  sold  it  for 
70i  regular.     Did  I  gain  or  lose,  and  how  much  ? 

4.  On  Dec.  1  D  bought  of  me,  through  C,  his  broker,  2000 
shares  of  Chicago,  Milwaukee  &  St.  Paul  at  99^  s.  60  (seller's 
option  any  time  within  60  da.).  On  Dec.  17  C,  pursuant  to  my 
instructions,  delivered  the  stock  which  he  had  purchased  for  me 
on  the  previous  day  at  96  regular.  Did  I  gain  or  lose,  and 
how  much  ? 


STOCKS  AND   BONDS 


417 


5.  Jan.  15  I  deposited  S4080  with  my  broker  and  instructed 
him  to  buy  400  shares  of  Baltimore  &  Ohio  whenever  he  could 
do  so  at  92  regular.  On  the  same  day  he  bought  the  stock  as 
directed.  On  Feb.  27  I  ordered  him  to  sell,  and  he  did  so  at 
95 1  cash.     What  was  my  net  gain  ? 

6.  May  25  a  speculator  sent  his  broker  a  margin  of  $2000 
with  which  to  buy  100  shares  Metropolitan  Street  Railway  at 
165  regular.  The  broker  invested  as  directed.  On  May  27 
the  stock  rose  to  170|  and  the  broker  was  authorized  to  sell. 
If  he  sold  regular  at  this  price,  what  was  the  speculator's  gain  ? 
the  broker's  commission? 

7.  What  is  the  balance  due  on  the  following  account  current: 


New  York,. 


lA^t 


f^  -j^^yf^  ^  T^.^^^^J^?-,^. 


yytr^i^/  ^./7 


-*9- 


^^^  -fyJr^^^.^.-^'^^ 


In  account  current  with 

RICHARD  ROE  &  C 

\o. 

DATE 

AMOUNT 

DAYS 

INTEREST 

DATE 

AMOUNT 

DAYS 

INTEREST 

7^t<zy 

/O 

/o 

>  ?  p 

// 

m 

>? 

Tfta^ 

/O 
2~S 

?f  ?  ?  ? 

CO 

// 

.'/ 

v 

PRODUCE  EXCHANGES 

497.  Just  as  there  are  stock  exchanges  in  many  of  the  large 
cities  to  supply  a  regular  market  for  the  purchase  and  sale  of 
securities,  so  there  are  produce  exchanges  (also  called  boards  of 
trade,  chambers  of  commerce,  etc.)  to  supply  a  regulated  market 
for  the  purchase  and  sale  of  farm  crops. 

Produce  exchanges  are  important  accessories  of  commerce.  They 
promote  jiist  and  equitable  principles  of  trade ;  establish  and  maintain  a 
uniformity  in  commercial  usages ;  and  acquire,  preserve,  and  disseminate 
valuable  business  information.  The  more  important  produce  exchanges, 
by  inspecting  and  grading  all  of  the  important  food  products,  protect  the 
public  against    fraud    and  adulterations.     The  cereals,  for  example,  are 


418  PRACTICAL   BUSINESS   ARITHMETIC 

inspected  and  graded  according  to  their  quality.  There  are  usually  four 
grades  of  wheat,  six  of  corn,  and  four  of  barley,  oats,  and  rye ;  No.  1  wheat 
is  the  best  quality,  No.  4,  the  poorest,  etc. 

The  principal  produce  exchange  in  the  United  States  is  the  Chicago  Board 
of  Trade.  On  the  floors  of  this  exchange  are  bought  and  sold  a  large  part 
of  the  cereals  and  the  meat  products  of  the  Mississippi  Valley  and  the 
West.  The  association  thus  practically  determines  the  price  of  these  com- 
modities, not  only  for  the  United  States,  but  for  the  world. 

Commodities  are  bought  and  sold  on  the  exchanges  for  present  or  for 
future  delivery.  Contracts  for  present  delivery  are  called  cash  contracts ; 
contracts  for  future  delivery,  futures.  Speculative  trading  in  grain  and. 
cotton  is  usually  in  "  futures." 

The  established  brokers'  commissions  on  the  Chicago  Board  of  Trade 
are  as  follows  :  for  grain,  $7.50  per  5000  bu. ;  for  pork,  -^  12.50  per  250  bbl. ; 
for  lard,  $15  per  250  tierces ;   for  ribs,  $12.50  per  50,000  lb. 

The  lowest  margins  received  are  :  Ope^.  High.  Low.  Clos. 

wheat,  5 /^^  per  bushel ;  corn  and  oats.       Wheat  —  July  ..  87        89^        87        88| 
3;*  per  bushel;  pork,  $1  per  barrel;      ^Slg^^ig       ^         «?j      ^| 

lard,  1 2  per  tierce ;  ribs,  ^f  per  pound.       Com —July 68|      68§        67f      68^ 

The  margins  demanded  are  some-      cornlDec*'  '"fi^      S^       ^^      5?f 
times  higher  than  the  above  figures.      Oats— July  . , . .  37|      37|        sil      37| 

In   the   accompanying    table   is      r=Dr::::Si      S|       ^f      f^ 
shown  the  opening,  highest,  lowest,      Pork— July   ...2120    2135     2120    2135 
and  closing  prices  of  provisions  for      Jr:^,ZfX::::To^    foil     To^    fo'^ 
a  certain  day  on  the  Chicago  Board      Lard— Sept.  ...  10 17    10  25     10  17    10  25 

of  Trfldp  Lard  — Oct 10  22     10  27       10  22     10  27 

Wr,  T-  Kibs- July  ....1152     1160       1150     1160 

"  Wheat  —  July  "  signifies  wheat      Ribs  —  Sept 11 52    11 57     11 52    11 57 

to  be  delivered  in  July ;  "  Wheat  —      ^^^ "  ^«* 11 30    11 35     11 30    11 35 

Sept."  wheat  to  be  delivered  in  September,  etc.  The  usual  time  for  future 
delivery  is  during  the  months  of  May,  July,  September,  and  December. 

In  the  following  exercise  it  is  assumed  that  all  transactions  are  effected 
through  a  broker,  who  charges  the  usual  commission. 

WRITTEN    EXERCISE 

1.  What  will  it  cost  me  to  buy  5000  bu.  September  wheat  at 
the  opening  price  in  the  table  ? 

2.  C  bought  10,000  bu.  July  oats  at  35/  per  bushel  and  sold 
the  same  at  the  closing  price  in  the  table.    What  was  his  net  gain  ? 

3.  B  bought  15,000  bu.  July  corn  at  the  lowest  price  and 
sold  the  same  at  the  highest  price  in  the  table.  Did  he  gain 
or  lose,  and  how  much  ?     What  per  cent  ? 


STOCKS   AND   BONDS  419 

4.  G  bought  2250  tierces  (765,000  lb.)  of  October  lard  at 
$  7.26|  and  sold  the  same  at  the  closing  price  in  the  table.  Did 
he  gain  or  lose,  and  how  much  ? 

5.  F  bought  1500  bbl.  of  September  pork  at  the  opening 
price  and  sold  the  same  at  the  closing  price  in  the  table.  Did 
he  gain  or  lose,  and  how  much  ? 

6.  D  ordered  his  broker  to  sell  5000  bu.  September  corn  and 
buy  5000  bu.  December  corn.  If  the  broker  sold  at  the 
highest  price  and  bought  at  the  lowest  price  in  the  table,  what 
amount  should  he  remit  D  ? 

7.  A  broker  bought  on  his  own  account  10,000  bu.  of  each, 
September  wheat,  December  corn,  and  July  oats,  at  the  opening 
price,  and  sold  the  same  at  the  closing  price  in  the  table.  Did 
he  gain  or  lose,  and  how  much  ? 

8.  H  sold  "  short "  10,000  bu.  September  wheat  at  the 
highest  price  in  the  table.  September  wheat  subsequently 
declined  to  85J  and  he  bought  at  this  price  to  "cover  his 
short."     Did  he  gain  or  lose,  and  how  much  ? 

9.  June  27  I  deposited  with  my  broker  a  margin  of  f  200  for 
the  purchase  of  5000  bu.  of  September  wheat  at  the  lowest 
price  in  the  table.  On  July  25  I  ordered  him  to  sell.  He 
did  so,  receiving  89|^  per  bushel.  How  much  should  he  pay 
me  in  settlement  ? 

10.    Aug.  5  I  deposited  with  my  broker  $2500  as  a  margin  for 
the  purchase  of  5000  bbl.  of  October  pork  at  the  closing  price 
in  the  table.     On  Sept.   2  I  ordered  him  to  sell  at  $13,071 
He  did  so   and  remitted  me    a   check   for   the   amount   due. 
What  w^as  the  amount  of  the  check  ? 


CHAPTER   XXXIV 

LIFE   INSURANCE 

498.  Life  insurance  companies,  like  fire  insurance  companies 
(page  278),  are  usually  either  stock  companies  or  mutual  com- 
panies. 

There  are  also  assessment  companies  and  fraternal  beneficiary  associa- 
tions. These  usually  depend  upon  monthly  assessments  or  "  calls  "  to  pay 
death  claims.  They  are  required  by  law  to  hold  but  comparatively  little, 
if  anything,  as  a  fund  from  which  to  pay  losses. 

499.  Insurance  rates  are  always  a  certain  price  per  $1000  of 
insurance.  They  are  payable  annually,  semiannually,  or 
quarterly  in  advance. 

500.  The  four  leading  kinds  of  policies  are  :  ordinary  life, 
limited  life,  endowment,  and  term. 

501.  An  ordinary  life  policy,  in  consideration  of  premiums  to 
be  paid  during  the  life  of  the  insured,  guarantees  to  pay  at  his 
death  a  stated  sum  of  money. 

502.  A  limited  life  policy,  in  consideration  of  premiums  to 
be  paid  for  a  fixed  number  of  years,  guarantees  to  pay  a  stated 
sum  of  money  at  the  death  of  the  insured. 

It  will  be  observed  that  in  an  ordinary  life  policy  the  premiums  are  pay- 
able during  the  life  of  the  insured,  while  in  a  limited  life  policy  they  are 
payable  for  a  fixed  number  of  years,  when  the  policy  becomes  paid  up  (no 
more  premiums  due).     The  premium  is  higher  on  the  latter  form  of  policy. 

503.  An  endowment  policy,  in  consideration  of  premiums 
paid  for  a  fixed  number  of  years,  guarantees  to  pay  a  stated 
sum  of  money  to  the  insured  at  a  certain  time  or  to  the  hene- 
jieiary  (one  in  whose  favor  the  insurance  is  effected)  in  case  of 
prior  death. 

504.  A  term  policy,  in  consideration  of  premiums  paid  for  a 
fixed  time,  guarantees  to  pay  a  stated  sum  of  money  if  the 
insured  dies  within  the  term  of  insurance. 

420 


LIFE   INSURANCE 


421 


Thus,  a  person  may  insure  his  life  for  a  limited  number  of  years  only. 
Since  the  company  may  never  be  called  upon  to  pay  the  insurance,  the 
premiums  on  these  policies  are  low. 

505.  The  reserve  is  that  part  of  the  premiums  of  a  policy, 
with  interest  thereon,  required  by  law  to  be  set  aside  as  a  fund 
to  be  used  in  payment  of  the  policy  when  it  falls  due. 

The  legal  rate  of  interest  on  reserve  funds  varies  slightly  in  different 
states.     The  higher  the  rate  of  interest,  the  smaller  tne  i.^erve  required. 

506.  The  surplus  of  an  insurance  company  is  the  excess  of 
its  assets  (resources)  over  its  liabilities. 

This  fund,  with  certain  restrictions,  may  be  used  for  such  purposes  as 
the  company  deems  best.  After  retaining  a  surplus  large  enough  to  pro- 
vide for  contingencies,  companies  which  issue  policies  on  the  mutual  or 
participating  plan  divide  the  remainder  of  the  surplus  among  such  of  its 
policyholders  as  are  entitled  to  share  in  it.  This  is  practically  a  return  of 
an  overcharge,  but  it  is  usually  called  the  payment  of  a  dividend. 

507.  Dividends  may  be  used:  (1)  to  reduce  the  next  year's 
premium  ;  (2)  to  purchase  additional  insurance,  payable  when 
the  policy  matures ;   (3)  to  shorten  the  time  to  run. 

Dividends  may  also  be  left  with  the  company,  with  the  distinct  under- 
standing that  there  shall  be  no  division  of  the  same  until  the  end  of 
a  certain  period.  As  the  policyholder  receives  no  benefit  unless  he 
surrives  the  selected  period,  it  will  be  seen  that  the  return  should  be  some- 
what larger.  This  plan  is  called  semi-tontine,  distribution  period,  accumu- 
lated surplus,  deferred  dividend,  etc. 

508.  If  a  policy  is  discontinued,  the  insured  may  secure  an 
equitable  return  for  the  reserve  accumulated. 

The  insured  usually  has  several  options  in  this  matter  :  (1)  he  may  take 
the  cash  value,  or  practically- all  of  the  reserve  value  of  the  policy;  (2)  he 
may  take  a  paid-up  policy  for  such  an  amount  as  its  reserve  value  will  pur- 
chase ;  (3)  he  may  take  extended  insurance  for  the  face  of  the  policy  for  as 
many  years  and  days  as  its  reserve  value  will  purchase. 

Annual  Premium  Rates  for  an  Insurance  of  $1000 


Age 

Ordinary 
Life 

20-Paymknt 
Life 

15-Year 
Endowment 

20- Year 
Endowment 

25 

20.93 

30.90 

66.57 

48.93 

30 

23.75 

33.76 

67.27 

49.72 

35 

27.39 

37.25 

68.26 

50.88 

40 

32.16 

41.60 

69.76 

52.70 

50     . 

47.23 

54.65 

76.20 

60.59 

422  PRACTICAL   BUSINESS   ARITHMETIC 

ORAL  EXERCISE 

1.  What  kind  of  a  policy  is  that  on  page  423  ?  Who  is  the 
beneficiary  ?   the   insured  ?      What   is   the   annual   premium  ? 

2.  Should  the  beneficiary  die  in  1912,  to  whom  would  the 
policy  be  payable  at  the  death  of  the  insured  in  1920  ? 

3.  Should  the  insured  die  after  having  paid  one  annual 
premium,  how  much  would  his  heirs  receive  ? 

4.  If  the  surplus  earnings  (dividends)  on  the  policy  amount 
to  $1200,  at  the  end  of  10  yr.,  how  much  cash  (see  page  424) 
would  the  insured  receive  should  he  surrender  the  policy  ? 

5.  Should  the  insured  decide  to  discontinue  paying  premiums 
after  making  five  annual  payments,  how  much  paid-up  in- 
surance, exclusive  of  the  surplus,  might  he  receive  ? 

6.  How  large  a  sum  may  the  insured  borrow  on  the  policy 
after  ten  premiums  have  been  paid  ? 

7.  If  the  company  secures  interest  in  advance  by  deducting 
it  from  the  amount  of  the  loan,  and  the  insured  should  borrow 
14000  for  one  year  at  5  %,  what  would  be  the  amount  of  the 
check  which  he  would  receive  from  the  company  ? 

8.  Had  the  insured  taken  out  the  policy  w^hen  he  was 
twenty-five  years  of  age,  what  would  be  the  annual  saving, 
exclusive  of  interest,  in  the  cost  ?  How  much  would  he  have 
saved  in  15  yr.  ?  in  20  yr.  ? 

9.  If  the  insured  should  discontinue  paying  premiums  after 
5  yr.  and  take  extended  insurance,  how  much  would  the 
beneficiary  receive  should  the  insured  die  in  1914?  in  1919? 

10.  If  the  insured  had  taken  a  life  policy  (see  rates,  page 
421)  for  the  same  amount,  instead  of  an  endowment  policy,  and 
died  after  having  paid  ten  full  premiums,  how  much  less  would 
his  insurance  have  cost,  exclusive  of  dividends  and  interest  ? 

11.  If  the  insured  should  pay  four  full  premiums  on  the 
policy,  take  extended  insurance,  and  die  5  yr.  later,  how  much 
would  his  beneficiary  receive  ? 

12.  If  the  insured  discontinues  making  payments  after  seven 
annual  premiums  had  been  paid,  how  much  would  he  get  in 
cash  at  the  end  of  20  yr.  from  date  of  issue,  if  living  ? 


LIFE   INSURANCE 


423 


/C>,(P^J2. 


in  Vw<0nSlClCri3.tl0n  of  the  Application  for  this  Policy,  hereby  made  a  part  of  this  contract. 

The  Penn  Mutual  Life  Iqsurance  Company  of  Philadelphia 

insures  the  life  of tOtOat^   f^.  ^ix6|?<>U  " 

in  the  County  of     'V^VOttl 


AGE 

SUM  INSURED 

YEARLY  PREMIUM 


ENDOWMENT 

IN    Z-0    YEARS 
Rettilar 


(INED  BY 
A.D.  yE4.  S.^«907 


of    UOCtt^^t^r        in  the  Counjty  of     '^^lOttfO^ 

in  the  sum  of T<Jtt  ^iV0U$Cinb*?fd^ 

to  pay  at  its  Home  Office,  in  the  City  of  Philadelphia,  unto    ' 


State  of     '?t^tO'50tfi  . 

Dollars,  and  promises 


-»ydc^' 


Th§  payment  in  advance  to  the  Company,  it  it 


-  executors,  administrators,  or  assigns,  the  said  sum  insured  on  the 
day  oiy_y^l€<l^     in  the  year  nineteen  hundred  and--?S^»*^2^^^-<^^^'^j?K- 
or  if  the  said  insured  should  di^efore  that  time  then  to  make  said  payment  to     ^ 

j^^^^^-^ ■ — . — . . 

executors,  administrators,  or  assigns,  upon  receipt  of  satisfactory  proof  of  the  death  of  the 
insured,  during  the  continuance  in  force  of  this  Policy,  upon  the  following  conditions,  namely  : 

its  Home  Office,  of  the  sum  of 
^  Dollars,  at  the  date  hereof,  and  of  the 

annual  premium  of  c^^^^^e.J^^^f<iii'«<^^:^^fe^:^C^\:^*»DollarSi 
at  or  before  three  o'clock  P.M.,  on  the     ^-^Ce^^^^^^  day  of    y_y4'Z'^l^ 

every  year  during  the  continuance  of  this  contract,  or  until 

^^>'€^J^  full  years'  premiums  shall  have  been  paid :  '--' — ' — " 

This  Policy  shall  participate  annually  in  the  surplus  earnings  of  the  Company  in  accord- 
ance with  the  regulations  adopted  by  the  Board  of  Trustees. 

The  extended  insurance,  paid-up  insurance,  and  loan  or  cash  surrender  value  privileges, 
benefits,  and  conditions  stated  on  the  second  page  hereof  form  a  part  of  this  contract  as  fully 
as  if  recited  at  length  over  the  signatures  hereto  affixed. 

In  Witness  Whereof,  The  Penn  Mutual  Life  Insurance  Company 

of  Philadelphia  has  caused  this  Policy  to  be  signed  by  its  President,  Secretai-y,  and 
Actuary,  attested  by  its  Registrar,  at  its  Home  Office,  in  Philadelphia,  Pennsylvania,  the 
-^^^i4^^  day  of         v-^^^y 


19  y 


/(Tc, 


Attest; 


-«-/iy 


Secretary 


egisttar 


^S^I^U^^^^r\     President 
"-^e^tc^.j^itt^uuy^        Actuary 


424 


PKACTICAL   BUSINESS  AElTHxMETIG 


Table  of  Extension,  Paid-up,  and  Loan  or  Cash  Values,  provided 
for  by  the  Policy,  if  no  indebtedness  exists  against  it 


AT 

END  OF 

YEAR 


TERM  OF  EXTENSION 
FOR  THIS  POLICY 


These'  Values  are  for  $1000  Insurance 

For  this  Policy  multiply  by /..U. 


PURE  ENDOWMENT  AT 
END  OF  EXTENSION 


PAID-UP  INSURANCE 
ON  SURRENDER 


LOAN  OR  CASH 
SURRENDER  VALUES 


^^  Years  Days 


jU^ 


XJl 


2U- 


U^ 


J^ 


^^4^ 


Z^ 


^r 


5th 


A£. 


^^ 


2=JjL 


J-Le. 


2=J^ 


Z^^ 


/J  / 


,^.3  2- 


7^  /.^ 


^A/^ 


AA. 


2-/  o 


3  r^A 


X^'f 


^ 


8tli 


AJ=. 


^rc 


^3  c 


3  C^  fo 


a£4- 


JJ^ 


,^./f 


4^^ 


7- 

^S-3  ^ 


J  j-c 


^ 


LCL 


^^^ 


A^(P 


4A/" 


-^^^^ 


S-<r7 


^^("^ 


S'aC 


12tli 


-r- 


rC  Z- 


A3A 


jr-^^^2-Z: 


-^ 


J=JA'. 


^  r/A 


:.£UL 


zr 


14th 


^  ru 


^z^ 


jLjUL 


^3- 


^£L 


7J/X 


7  7  7 


(^  7^  <P^ 


J^ 


-^21^^ 


t^^ 


-i^ 


74- 


IVth 


^ 


<t.r/ 


^  (7  Z- 


/-^^ 


-^ 


Z:^ 


7^C 


^3^ 


rc  / 


o  / 


19th 


^  j-z 


^3~<^ 


<:? zr  C7 / 


Ml 


(^^^C(to0 


/-OjUL 


^Ul. 


Should  any  indebtedness  exist  it  shall  be  deducted  from  the  Cash  Value  of  the  Policy, 
and  the  other  values  shall  be  diminished  proportionately 


LIFE  IKSURANCE  425 

WRITTEN  EXERCISES 

1.  If  the  insured  in  the  foregoing  policy  should  die  just  be- 
fore the  twelfth  payment  was  due,  how  much  would  the  estate 
receive  above  his  total  payments  ? 

2.  Suppose  that  the  insured  in  the  foregoing  policy  survives 
the  endowment  period,  and  the  surplus  earnings  of  the  policy 
amounted  to  #3500.  What  would  be  the  difference  between  the 
amount  received  and  the  amount  paid,  not  reckoning  interest  ? 

3.  The  insured  in  the  foregoing  policy  took  out  a  110,000 
20-payment  life  policy  at  the  same  time  he  procured  his  endow- 
ment policy.  The  guaranteed  cash  value  on  the  former  was 
$2557.80  at  the  end  of  10  yr.,  and  the  dividends  for  this  term 
amounted  to  883.22  per  thousand.  If  the  dividends  on  the 
endowment  policy  for  this  period  amounted  to  i  127.83  per  thou- 
sand, which  would  have  been  the  better  investment,  interest  not 
being  considered,  and  how  much  ? 

4.  Assuming  that  the  insured  in  the  foregoing  policy  survived 
the  endowment  period  and  that  the  dividends  which  amounted 
to  f  350  per  thousand  were  used  to  add  to  the  value  of  the  pol- 
icy, how  much  less  would  he  receive  from  the  company  than  he 
would  from  investing  the  amount  of  the  premiums  in  a  savings- 
bank  annually  for  20  yr.  at  4  %  interest?    (Use  table,  page  323.) 

5.  What  will  be  the  first  annual  premium  on  a  f  15,000  ordi- 
nary life  policy  for  a  man  50  yr.  old  ? 

6.  On  his  25th  birthday  A  took  out  a  20-yr.  endowment 
policy  for  $5000 ;  on  his  35th  birthday,  a  15-yr.  endow- 
ment policy  for  16000;  on  his  40th  birthday,  a  20-payment 
life  policy  for  $10,000.  He  died  aged  43  yr.,  6  mo.  How 
much  more  did  his  heirs  receive  (dividends  excepted)  than  he 
had  paid  the  company  ? 

7.  B  at  the  age  of  25  yr.  took  out  a  20-payment  life  policy 
for  $5000.  He  died  just  before  his  twentieth  payment  became 
due.  The  company  allowed  $87.50  per  thousand  in  dividends 
during  this  period,  and  these  were  used  to  reduce  the  annual 
premium.  How  much  more  did  his  heirs  receive  than  was  paid 
in  premiums  ? 


PAKTITIVE     PROPORTION,     PARTNERSHIP, 
AND     STORAGE 

CHAPTER   XXXV 

PARTITIVE   PROPORTION  AND  PARTNERSHIP 
PARTITIVE   PPvOPORTION 

ORAL   EXERCISE 

1.  A  fails  in  business  owing  D  ^500,  E  11500,  and  F  $2500. 
If  his  resources  are  $1800,  how  much  can  he  pay  each  of  his 
creditors  ? 

2.  Two  brothers,  A  and  B,  are  engravers.  .  A  can  earn  $10 
per  day  and  B  $5  per  day.  How  much  can  they  both  earn  in 
a  day  ?     What  part  of  this  amount  can  B  earn  ?     A  ? 

3.  They  formed  a  partnership  for  one  year  and  agreed  to 
divide  the  net  profits  in  proportion  to  the  earning  capacity  of 
each.  If  the  net  profits  for  the  year  were  $3600,  what  was  the 
share  of  each  ? 

4.  C  invests  $3000,  B  $6000,  and  A  $9000  in  a  manufacturing 
plant.  The  net  profits  for  one  year  are  $3600,  and  this  sum  is 
shared  in  proportion  to  the  amount  of  capital  invested.  What 
amount  does  each  receive  as  his  share  of  the  net  profits  ? 

5.  A  certain  street  was  paved  at  a  cost  of  $3000.  The  prop- 
erty owners  on  the  street  were  A,  who  owned  200  ft.  frontage, 
B,  who  owned  400  ft.  frontage,  and  C,  who  owned  600  ft.  front- 
age. If  the  cost  of  the  paving  was  assessed  on  the  property 
owners  in  proportion  to  the  frontage  owned,  how  much  did 
each  pay  ? 

509.  The  process  of  dividing  a  number  into  parts  propor- 
tional to  several  given  numbers  is  called  partitive  proportion. 

426 


PARTITIVE   PROPORTION   AND   PARTNERSHIP      427 

WRITTEN  EXERCISE 

1.  Divide  $42,770  among  G,  H,  and  I  in  proportion  to  J,  J, 
and  ^,  respectively. 

Suggestion,  -i,  |,  and  |-  =  |,  |,  and  i,  respectively.  Therefore,  i,  i,  and 
I  stand  in  the  same  relation  to  each  other  as  |,  f,  and  \,  or  as  2,  4,  and  1. 

2.  Divide  the  simple  interest  on  f  72,000  for  1  yr.  7  mo.  at 
3|-%  among  D,  E,  and  F  so  that  D's  part  will  be  twice  E's  part 
and  one  half  of  F's  part. 

3.  An  inheritance  of  $75,000  was  divided  among  3  sons  and 
4  daughters,  so  that  each  daughter  received  ^  more  than  each 
son.     How  much  did  each  son  receive  ?  each  daughter  ? 

4.  A,  B,  and  C  w^ere  partners  in  a  business.  A  put  in 
110,000,  B  $6000,  and  C  $9000.  Their  net  gain  for  a  year  was 
$17,500,  shared  in  proportion  to  the  amount  of  capital  invested. 
What  was  each  partner's  share  of  the  net  gain  ? 

PARTNERSHIP 

ORAL   EXERCISE 

1.  I  invested  $  500  in  a  business  and  during  the  first  year 
gained  $  1100.  No  withdrawals  or  subsequent  investments 
having  been  made,  what  was  my  present  worth  at  the  close  of 
the  year  ? 

2.  Jan.  1  M  invested  $  7500  in  a  factory.  July  1  he  found 
that  his  net  loss  was  $  1125.  What  was  his  present  worth 
July  1,  no  withdrawals  or  subsequent  investments  having  been 
made  ? 

3.  Answer  problem  1  assuming  that  there  was  a  withdrawal 
of  $  800  made  during  the  year ;  problem  2  assuming  that  there 
was  a  subsequent  investment  of  $  1200  made  on  Mar.  1. 

4.  Apr.  1  B  commenced  business  with  a  cash  investment  of 
$  1500  ;  Jan.  1  of  the  next  year  his  present  worth  was  $  1875. 
What  was  his  net  gain  or  loss,  no  withdrawals  or  subsequent 
investments  having  been  made  ? 


428  PRACTICAL   BUSINESS   ARITHMETIC 

5.  July  1  D  began  business  investing  $25,000;  Jan.  1  of 
the  next  year  his  net  capital  was  $  23,150.  If  no  withdrawals 
or  subsequent  investments  were  made,  did  he  gain  or  lose,  and 
how  much  ? 

6.  Answer  problem  4  assuming  that  there  were  withdrawals 
amounting  to  i  1000  ;  problem  5  assuming  that  there  was  a 
subsequent  investment  of  f  5000. 

7.  June  1  F  began  business  with  a  capital  of  $  1750. 
During  the  6  mo.  following  he  lost  $  2750.  What  was  the 
condition  of  his  business  Dec.  1  ? 

8.  Z  began  business  on  July  1  Avith  a  capital  of  $  2500. 
6  mo.  later  his  net  insolvency  was  found  to  be  $  1250.  What 
was  his  net  gain  or  loss  ? 

9.  A's  business  was  insolvent  $1250  on  Jan.  1.  From 
Jan.  1  to  July  1  he  gained  $1750.  What  was  the  condition 
of  his  business  July  1  ? 

10.  G  gained  f  3750  during  a  certain  year.  He  then  found 
that  his  net  capital  was  $1250.  What  was  the  condition  of 
his  business  at  the  beginning  of  the  year? 

11.  June  30,  1915,  C's  resources  were  $  7500  and  his  liabili- 
ties $5000.  June  30,  1916,  his  resources  were  $5000  and  his 
liabilities  $  7500.  What  was  his  net  gain  or  loss  during  this 
period  ? 

12.  Were  the  conditions  in  problem  11  reversed  for  the  year 
stated,  what  would  be  the  net  gain  or  loss  ? 

13.-   What  is  meant  by  resources?   liabilities?  gain?   loss? 

14.  What  is  meant  by  net  gain?  net  loss?  present  ivorth? 
net  capital?   net  insolvency? 

15.  Read  aloud  the  following,  supplying  the  missing  words: 

The  condition  of  the  business  at  the  beginning  +  the 

or  —  the =  the   condition  of   the  business   at  the 

close  ;    and    conversely,  the  condition   pf   the  business  at  the 

close  +  the or  —  the =  the  condition  of 

the  business  at  the  beginning. 


PARTITIVE   PROPORTION  AND   PARTNERSHIP      429 

510.  A  partnership  is  an  association  of  two  or  more  persons 
who  have  agreed  to  combine  their  labor,  property,  and  skill, 
or  some  of  them,  for  the  purpose  of  carrying  on  a  common 
business  and  sharing  its  gains  and  losses. 

Partnerships  may  be  formed  by  either  an  oral  or  a  written  agreement,  and 
in  some  cases  by  implication  ;  but  all  important  partnerships  should  be 
entered  upon  by  an  agreement  in  writing  which  definitely  states  all  of  the 
conditions  relating  to  the  business. 

511.  The  members  of  a  partnership  are  called  partners. 

Partners  may  be  divided  into  four  classes :  (1)  Real,  or  ostensible,  those 
who  are  known  to  the  world  as  partners  and  who  in  reality  are  such ; 
(2)  nominal,  those  who  are  known  to  the  world  as  partners  but  who  have 
no  investment  and  receive  no  share  of  the  gain  ;  (3)  dormant,  or  silent, 
those  who  are  not  known  to  the  world  but  who  nevertheless  partake  of  the 
benefits  of  the  business  and  thereby  become  partners;  (4)  limited,  or 
special,  those  whose  liability  is  limited. 

Nominal  partners,  like  real,  or  ostensible,  partners,  are  liable  to  third 
parties  for  the  debts  of  a  business.  Dormant  partners  are  liable  for  the 
debts  of  the  business  as  soon  as  their  partnership  connections  become  known 
to  the  world. 

Ordinarily  each  partner  is  liable  for  all  of  the  debts  of  the  firm,  but  a 
special  partner's  liability  is  limited  usually  to  the  amount  which  he  con- 
tributes to  the  firm's  capital. 

The  method  of  forming  a  limited  partnership  is  prescribed  by  statute. 
This  differs  somewhat  in  the  different  states.  Such  a  partnership  must 
usually  have  at  least  one  member  whose  liability  is  not  limited  and  who  i& 
the  manager  of  the  business. 

512.  The  capital  of  a  partnership  constitutes  all  the  moneys 
and  other  properties  contributed  by  the  different  partners  to 
carry  on  the  business. 

Gains  and  Losses  Divided  Equally 

513.  The  gains  and  losses  of  a  business  are  divided  among 
the  partners  in  accordance  with  the  agreement  or  contract  en- 
tered into  when  the  partnership  was  formed.  If  the  partners 
invest  equal  sums  and  contribute  equally  in  work,  the  gains  are 
usually  divided  equally. 


430 


PRACTICAL   BUSINESS   ARITHMETIC 


WRITTEN  EXERCISE 


1.    Copy  and  complete  the  following  ledger  page 


"^    Ui^^ 


Jo 


JIZZ^ 


A.^U'^t.^Oh-H^ 


JJ- 


LLLL 


2^.-7^ 


LL. 


.  %^^^t^J 


LL 


LL 


Uty> 


Ucm.  Jo 


;6  'ajA^ 


ro(?o 

LLL 


/  /  /  / 


?  r  F  F 


rooo 

?  ?  ? 


/  /  /  / 


// 


//» 


In  solving  problems  2-4  use  ledger  paper  as  above. 
If  the  student  is  not  familiar  with  simj^le  accounts,  pages  41-47  should 
be  reviewed. 

2.  Jan.  1,  1915,  C.  B.  Johnson  and  B.  H.  Briggs  engaged  in 
a  partnership  business,  each  investing  $3750.  July  1,  1915, 
each  partner  withdrew  1 250.  Jan.  1,  1916,  their  losses  and 
gains  were  as  follows  :       • 

Losses  Gains 

Expense  $104.75      Merchandise  $628.45 

Merchandise  Discounts  24.20      Interest  and  Discount  133.50 

Real  Estate  250.60      Stocks  and  Bonds  190.50 

What  was  the  present  worth  of  each  partner  Jan.  1,  1916? 


PARTITIVE   PROPORTION   AND  PARTNERSHIP      431 

3.  A,  B,  and  C  were  partners  for  a  year.  Each  invested 
89500  and  during  the  continuance  of  the  partnership  each  with- 
drew rj^lOOO.    The  losses  and  gains  at  closing  were  as  follows  : 


Losses 

Gains 

Merchandise  Discounts 

$18.90 

Merchandise 

$4375.80 

Expense 

650.00 

Interest  and  Discount 

90.14 

What  was  the  net  capital  of  each  at  closing  ? 

4.  O,  P,  and  Q  are  partners  sharing  the  gains  and  losses  in 
equal  proportions.  O  invested  18500,  P  $8200,  and  Q  'f  8450. 
During  their  first  year  the  gains  were  as  follows :  merchandise, 
16457.10;  real  estate,  1680.50  ;  interest  and  discount,  129.90. 
If  the  cost  of  conducting  the  business  was  $1920.50,  what  was 
the  present  worth  of  each  partner  at  the  end  of  the  year  ? 

Gains  and  Losses  Irregularly  Divided 

514.  Sometimes  the  gains  are  divided  according  to  certain 
arbitrary  fractions  which  are  not  in  proportion  to  the  amount 
invested.  In  such  cases  the  skill  of  a  partner  is  frequently 
considered  as  being  equal  to  a  certain  amount  of  capital.  In 
some  cases  a  certain  amount  is  paid  the  heavier  investor 
before  other  division  of  the  gains  or  losses  is  made.  In  still 
other  cases,  a  stated  salary  is  paid  to  each  partner  before  the 
gains  or  losses  of  the  business  are  divided.  This  salary  varies 
according  to  the  ability  of  the  several  partners  or  according  to 
the  time  each  devotes  to  the  business. 

WRITTEN  EXERCISE 

1.  A  and  B  entered  into  partnership,  each  investing  $  7500. 
Because  of  the  greater  experience  of  A  he  was  to  be  credited 
with  81200  before  any  other  division  of  the  gains  or  losses. 
The  gains  or  losses  were  then  to  be  divided  equally.  During 
the  first  year  the  gains  were  as  follows  :  merchandise,  §4111.10  ; 
real  estate,  1510.  If  the  losses  were  i  622.80,  what  was  the 
present  worth  of  each  at  the  end  of  the  year  ? 


432  PRACTICAL   BUSINESS   ARITHMETIC 

2.  A  and  B  entered  into  partnership,  A  investing  1 8000  and 
B  110,000.  B  doing  no  work,  it  was  agreed  that  A  should  take 
$  2000  from  the  gains  before  dividing,  and  that  the  net  gain  or 
loss  should  then  be  shared  equally.  The  gains  last  year  were 
18900  and  the  losses  ^1400.     What  was  the  net  gain  of  each? 

3.  C,  D,  and  E  entered  into  partnership  Jan.  1,  each  in- 
vesting 18500.  The  articles  of  agreement  provided  (1)  that 
C  should  devote  all  his  time  to  the  business  and  D  and  E  only 
a  portion  of.  their  time  ;  (2)  that  if  losses  occurred,  they  should 
be  borne  equally;  (3)  that  if  gains  were  realized,  C  should 
receive  J  and  D  and  E  each  J.  During  the  year  the  gains 
were  as  follows:  Merchandise,  $8217.10;  Stocks  and  Bonds, 
1612.50;  Interest,  .$492.92.  If  the  expenses  were  $2,217.80, 
what  was  the  present  worth  of  each  partner  at  the  close  of  the 
year  ? 

4.  F  and  G  entered  into  partnership,  F  investing  $5000  and 
G  $7500.  Because  of  the  greater  skill  of  F  it  was  agreed  that 
he  should  be  credited  with  $  1500  a  year  before  other  division  of 
the  gains  or  losses.  Then  if  losses  occurred,  F  was  to  bear  |  of 
them  and  G  f  ;  but  if  gains  were  realized,  they  were  to  be 
divided  equally.  During  the  first  year  the  gains  of  the  firm 
were  as  follows  :  Merchandise,  $3129.50  ;  Real  Estate,  $250  ; 
Stocks  and  Bonds,  $575  ;  Interest,  $130.50.  If  the  cost  of 
conducting  the  business  was  $938.48  (exclusive  of  F's  salary), 
what  was  each  partner's  net  capital  at  the  close  of  the  year  ? 

5.  J,  K,  and  L  entered  into  partnership,  J  investing 
$20,000,  K  $10,000,  and  L  nothing.  The  articles  of  agreement 
provided  (1)  that  the  gains  or  losses  should  be  shared  as 
follows  :  J,  |,  K,  ^,  L,  2%  ;  (2)  that  the  capital  should  be  kept 
intact ;  (3)  that  before  any  division  of  the  profits  was  made,  J 
should  be  credited  with  an  annual  salary  of  $  1500.  At  the 
end  of  a  year  the  resources  were  found  to  be  $65,250  and  the 
liabilities  (not  including  J's  salary),  $16,750.  What  was  each 
partner's  share  of  the  net  gain  ?  After  the  net  gain  was 
credited,  what,  was  the  net  capital  of  each  partner  ? 


PARTITIVE   PROPORTION   AND   PARTNERSHIP     433 


Gains  and  Losses  Divided   According   to   Investment 

515.  Sometimes  the  gains  and  losses  are  divided  in  propor- 
tion to  the  amount  invested  ;  that  is,  according  to  the  princi- 
ples of  partitive  proportion. 

516.  Example.  A  and  B  engaged  in  business,  agreeing  to 
share  the  gains  or  bear  the  losses  in  proportion  to  the  amount 
of  capital  invested.  A  invested  $2500  and  B  13500.  They 
gained  $1800.     What  was  the  share  of  each? 

Solution.  $2500  +  $  8500  =  $  6000,  the  total  capital.  Since  the  total  capital 
is  $6000  and  A  put  in  $2500,  A's  share  is  |fg§,  or  j%,  and  B's  share  is  |§g§,  or 
j'j.  Therefore,  A  should  receive  j\  of  $  1800,  or  $  750,  and  B  should  receive 
j7^  of  $  1800,  or  $  1050. 

ORAL   EXERCISE 

Find  each  maris  gain  or  loss  in  each  of  the  following  problems : 
Investment  Gain  Investment  Loss 

1.  A,  $3000;  B,  12000     1500  6.  K,$2000;  L,i4000  |120 

2.  C,  $1000;  D,$2000     $150  7.  M,$1500;  N,$2000  $700 

3.  E,$1200;  F,  $4800   $1200  8.  O,$1000;  P,$5000  $600 

4.  G,$1500;  H,  $4500  $1800  9.  Q,$1500;  R,$6000  $750 

5.  I,  $1500;  J,  $7500  $1500  lo.  S,  $1750;  T,$3500  $600 


written  exercise 

1.  A,  B,  and  C  invested  $2000,  $3000,  and  $5000,  respec- 
tively, in  a  wholesale  dry  goods  business.  During  the  first  year 
the  net  profits  were  $4155.80.     What  was  the  share  of  each  ? 

2.  D,  E,  and  F  invested  $2500,  $3250,  and  $3500,  respec- 
tively, in  a  manufacturing  business.  At  the  close  of  the  first 
year  their  profits  were  found  to  be  $3774.37.  What  was  the 
share  of  each  ? 

3.  G,  H,  and  I  formed  a  copartnership,  G  investing  $3000, 
H,  $2000,  and  I,  $1500.  During  the  first  six  months  their  net 
gain  was  $1829.10.  How  much  was  each  man  worth  after  his 
share  of  the  net  gain  had  been  carried  to  his  account  ? 


434  PEACTICAL  BUSINESS  AKITHMETIG 

4.    Copy  and  complete  the  following  statement : 


C?^/^- 


C^r^r^^S'i.^C.'^d.'^^  '/j  ^  .->v^..'i^<!i..'i^-j'Z^ 


n  r> 


<<ii>i,.t-£.--7^l^ 


--;^'^.<i<^,^<?^-^=>i*/T7^''€^?C-^ 


G.^^^/r^&^€.^d.d.c.c:j 


'^^^.d,^^ylJ-Mb^^-tAy        <7^.^cA^-^U^^^^ 


^zyusc 


SSf2- 


/or 


/JO? 


/Cj-r 
2-oCj 


SXZJSO 


???? 


nn 


^roo 


n 


jsrz 


J?7 


sj-g-z 


j-o 


/J  Of 


A^lJTO 


J-Z2J'Sc? 


"^rQo 


PARTITIVE  PROPORTION  AND  PARTNERSHIP    435 

Interest  Allowed  and  Charged 

517.  The  inequalities  in  investments  and  withdrawals  are 
frequently  adjusted  by  allowing  and  charging  interest  upon 
same.  When  interest  is  allowed  on  investments  and  charged 
on  withdrawals,  the  gains  and  losses  are  usually  divided 
equally. 

518.  Example.  June  1,  1915,  C.  H.  Dean  and  E.  D.  Snow 
formed  a  partnership,  C.  H.  Dean  investing  $  5000  and  E.  D. 
SnoAV  $  4000.  They  agreed  that  the  gains  and  losses  should  be 
divided  equally,  but  that,  owing  to  the  unequal  investments, 
each  partner  should  be  allowed  interest  at  6  %  on  all  sums 
invested  and  charged  interest  at  the  same  rate  on  all  sums 
withdrawn,  said  interest  to  be  adjusted  at  the  time  of  closing 
the  books.  The  profits  for  the  first  six  months  were  $  1050. 
What  was  the  net  capital  of  each  partner  after  the  interest  was 
adjusted  and  the  net  gain  carried  to  his  account  ? 


c. 

H. 

Dean 

1915 
Dec. 

1 

Net  Capital 

5540 

00 

1915 
June 
Dec. 

1 
1 

1 

Investment 
Interest 
i  Net  Gain 

Net  Capital 

5000 

15 

525 

00 
00 
00 

5540 

00 

5540 

00 

Dec. 

1 

5540 

00 

E. 

D. 

Sn 

OW 

1915 

Dec. 

1 
1 

Interest 
Net  Capital 

15 
4510 

00 
00 

1915 
June 

1 
1 

Investment 
^  Net  Gain 

Net  Capital 

4000 
525 

00 
00 

4525 

00 

4525 
4510 

00 

Dec. 

1 

00 

Solution.     $  5000  in  6  mo.  will  earn  $  150  interest. 
$  120    interest. 


4000  in  6  mo.  will  earn 


^150  +  #120  -T-  2  =  $135,  the  average  interest  earned. 
$150  —  $135  =  $15  ;  that  is,  C.  H.  Dean's  interest  is  $15  above  the  average. 
$135  -  $120  =  $  15  ;  that  is,  E.  D.  Snow's  interest  is  $15  below  the  average. 
Therefore  to  adjust  the  interest  on  the  investments,  credit  C.  H.  Dean's  ac- 
count $  15  and  charge  E.  D.  Snow's  account  $  15.  ^  of  $  1050  =  $  525,  the  net 
gain  of  each.  Credit  each  account  with  the  net  gain  ;  then  C.  H.  Dean's  net 
capital  is  $5540  and  E.  D.  Snow's  net  capital  $4510. 


436 


PKACTICAL   BUSINESS   ARITHMETIC 


WRITTEN    EXERCISE 

1.    Copy  and  complete  the  following  statement  of  conditions; 


'3/,/^- 


?hi//^i/^2.'C-u^'y^ 


^/oooo 


»  )t 


10 


3CC 

1^33 


/0S-O 


<frj-c 


??fn 


2J  i-OCefjn 


'  /  / .'  / 


yzof 


SiP 


PAETITIVE   PROPORTION   AND   PARTNERSHIP     437 


2.  W.  H.  Burgess  and  Otis  Clapp  began  business  July  1, 
1915,  the  former  investing  $12,000  and  the  latter  $10,000. 
They  agreed  that  the  gains  and  losses  should  be  divided  equally, 
but  that,  because  of  the  inequality  in  the  investments,  interest 
at  6  %  should  be  allowed  on  investments  and  charged  on  with- 
drawals. July  1,  1916,  the  firm's  resources  and  liabilities 
(partners'  accounts  excluded)  were  as  follows  : 


Resources 

Liabilities 

Cash 

$4150.00 

Accounts  Pay. 

$7500. 

Accounts  Rec. 

8150.60 

Notes  Pay. 

4900. 

Mdse. 

18210.50 

Notes  Rec,  on  hand 

4250.00 

Street  Railway  Stock 

3000.00 

Store  and  Lot 

5200.00 

Office  Fixtures 

500.00 

Make  a  statement,  as  in  problem  1,  showing  the  present  con- 
dition of  the  business. 

3.  Aug.  1,  1915,  F.  E.  Greene  and  W.  B.  Linden  formed  a 
partnership  for  the  purpose  of  carrying  on  a  manufacturing 
business.  F.  E.  Greene  invested  18500  and  W.  B.  Linden, 
810,750.  It  was  agreed  that  interest  at  6%  should  be  allowed 
and  charged  on  investments  and  withdrawals  and  that  the  gains 
and  losses  should  be  divided  equally.  At  the  close  of  the  first 
year  the  resources  and  liabilities  (partners'  accounts  excluded) 
were  as  follows : 


Liabilities 
Notes  Pay.  $1158.25 

Accounts  owed  by  the  busi- 
ness 2100.00 


Resources 
Cash  $2355.20 

Mdse.  5284.85 

Notes  Rec.  2840.00 

Accounts  owing  the  business  4170.50 
Office  Fixtures  450.00 

Feb.  1,  1916,  F.  E.  Greene  withdrew  1750  and  W.  B.  Linden 
i600.  Make  a  statement  showing  the  condition  of  the  business 
at  the  close  of  the  year. 

4.  James  B.  Westfall  and  John  L.  Manning  began  a  common 
business  on  Sept.  1,  1915,  the  former  investing  $14,500  and 
the  latter  $13,935,     They  agreed  that  interest  at  6^  should  be 


438 


PRACTICAL   BUSINESS   ARITHMETIC 


allowed  and  charged  on  investments  and  withdrawals,  respec- 
tively, and  that  the  gains  and  losses  should  be  divided  equally. 
Sept.  ,1,  1916,  a  trial  balance  of  their  general  ledger  was  as 
follows  : 


Debits 

Credits 

James  B.  Westfall 

$14500.00 

John  L.  Manning 

1  935.00 

Cash 

1^13368.64 

Merchandise 

31664.00 

20000.00 

Office  fixtures 

510.50 

Horse  and  wagon 

405.00 

Real  estate 

7000.00 

Expense 

445.80 

Collection  and  exchange 

12.20 

Mdse.  discounts 

58.50 

Accounts  receivable 

6852.84 

Accounts  payable 

8864.75 

Bills  payable 

3000.00 

Interest  and  discount 

' 

17.73 

$60317.48 

160317.48 

The  merchandise  unsold  was  found  to  be  worth  $13,827.35  ; 
the  real  estate,  17500  ;  the  office  fixtures,  1500  ;  the  horses  and 
wagons,  1400;  and  the  expense  items  on  hand,  1102.50.  There 
was  due  on  the  merchandise  account  for  freight,  f  138.50,  and 
on  the  expense  account  for  telephone  service,  $25.  Make  a 
statement  showing  the  condition  of  the  business  Sept.  1,  1916. 
(See  model,  page  441.) 

Gains  and  Losses  Divided  According  to  the  Average 

Investment 

519.  That  sum  which,  invested  for  a  certain  period,  is 
equivalent  to  two  or  more  sums  invested  for  different  periods, 
is  called  an  average  investment.  The  gains  and  losses  of  a 
business  are  sometimes  divided  in  proportion  to  the  average 
investment. 

520.  Example.  April  1,  1915,  A  and  B  formed  a  partner- 
ship and  agreed  to  share  the  gains  or  losses  according  to  aver- 
age net  investment.     A  furnished  110,000  of  the  capital  and 


PARTITIVE   PROPORTION  AND   PARTNERSHIP      439 

B$7500.  July  1  A  withdrew  81500  and  B  $500.  Apr.  1, 
1916,  their  net  gain  was  found  to  be  112,800.  What  was 
the    net   gain   of   each   partner  ? 

Solution 
A  had  in  310,000  for  3  mo.,  when  he  withdrew  $1500,  leaving  8  8500  for  the 
remaining  9  mo. 

B  had  in  $7500  for  3  mo.,  when  he  witlidrew  $ 500,  leaving  $7000  for  the 
remaining  9  mo. 

A's  $10000  for  3  mo.  =  $30000  for  1  mo. 

A's  $8500  for  9  mo.  =  $76500  for  1  mo. 

A's  average  net  investment  =  $106500  for  1  mo. 
B's  $7500  for  3  mo.  =  $22500  for  1  mo. 

B's  $7000  for  9  mo.  =  $03000  for  1  mo. 

B's  average  net  investment     =  $85500  for  1  mo. 
$106500  +  $85500  =  $192000,  the  firm's  average  net  investment  for  1  mo. 

A'sshareisiaft-og,  or.Vs- 

B's  share  is  ^^2^.  or  ,%\. 

Therefore,  A  should  receive  yV^  of  $12800,  or  $7100. 

And  B  should  receive  j\\  of  $  12800,  or  $5700. 

WRITTEN  EXERCISE 

1.  Apr.  1  R  and  C  formed  a  partnership  for  1  yr.,  the 
former  investing  14500  and  the  latter  $6000.  They  agreed 
to  share  the  gains  and  losses  in  proportion  to  the  average  net 
investment.  Aug.  1  R  invested  il500,  and  C  withdrew  11000. 
On  closing  the  books  at  the  end  of  the  year  the  net  loss  was 
found  to  be  81290.  What  was  each  partner's  present  worth 
after  his  account  was  charged  with  his  share  of  the  net  loss  ? 

2.  June  1,  1915,  E  and  F  formed  a  copartnership  for  the 
purpose  of  carrying  on  a  real  estate  business.  E  invested 
1)25,000  and  F  |15,000.  They  agreed  to  share  the  gains  and 
losses  in  proportion  to  the  average  net  investment.     Sept.  1, 

1915,  E  withdrew  81000  and  F  1500.  Dec.  1,  1915,  each 
withdrew  81000.     Mar.  1,  1916,  F  invested  85000.     June  1, 

1916,  the  partnership  was  dissolved.  After  all  resources  were 
converted  into  cash  and  all  liabilities  to  outside  parties  paid, 
the  amount  of  cash  in  bank  was  850,890.  What  amount  was 
due  each  partner? 


440  PRACTICAL   BUSINESS   ARITHMETIC 

WRITTEN  REVIEW  EXERCISE 

1.  Apr.  1,  1916,  W.  L.  Cutter  and  O.  M.  Woodward  formed 
a  copartnership  for  the  purpose  of  carrying  on  a  dry  goods 
business.  W.  L.  Cutter  invested  120,500  and  O.  M.  Wood- 
ward 818,500.  They  agreed  to  allow  interest  at  6%  on 
investments,  charge  interest  at  the  same  rate  on  withdrawals, 
and  divide  the  gains  and  losses  equally.  July  1,  1916,  W.  L. 
Cutter  withdrew  |500.  Oct.  1  O.  M.  Woodward  withdrew 
11000  and  W.  L.  Cutter  $750.  At  the  close  of  the  year  the 
resources  and  liabilities,  exclusive  of  partners'  accounts,  were 
as  follows  : 


Resources 

Liabilities 

Cash  in  bank 

$2130.60 

Accounts  owed  by  the  busi- 

Stocks and  bonds  on  hand 

6450.00 

ness                                      17260.00 

Goods  in  stock 

16095.00 

Notes  payable  unredeemed     1200.00 

Notes  receivable  on  hand 

6150.00 

Office  fixtures  on  hand 

500.00 

Accounts  owing  the  busi- 

ness 

12260.52 

Make  a  statement  showing  the  condition  of  the  business 
Apr.   1.   1917. 

2.  July  1,  1915,  A.  B.  Curtis  and  B.  H.  Barton  formed  a 
partnership  and  invested  $7500,  of  which  A.  B.  Curtis  fur- 
nished I  and  B.  H.  Barton,  |.  Jan.  30,  1916,  their  resources 
were  as  follows  :  merchandise,  unsold,  $  2172.70  ;  cash  on 
hand,  12823.96;  real  estate  on  hand,  rf3100;  account  against 
James  Noble,  1840.10;  account  against  A.  H.  Cook  &  Co., 
$  1156.84.  On  the  same  date  their  liabilities  were  as  follows  : 
account  in  favor  of  D.  M.  Frost  &  Co.,  1218.60;  account 
in  favor  of  J.  B.  Neal  &  Co.,  1385.  During  the  year  the 
merchandise  bought  cost  $6807.50  and  the  sales  aggregated 
$7154.90.  The  cost  of  carrying  on  the  business  was  $530.10. 
Make  a  statement  (see  page  434)  showing  the  present  condi- 
tion of  the  business.  Divide  the  net  gain  in  proportion  to  the 
investments. 


PARTITIVE   PROPORTION   AND   PARTNERSHIP      441 
3.    Copy  and  complete  the  following  statement  of  conditions: 


3/,/f. 


/zr7^ii2. 


/reyg-  /o 


■^U^U.^'yiJ-Th?',^^^ 


2.o/j'£>  ro 


? ' '  > 


Trryi/ 


/yior 


Cryzi^ 


6,x 


Cz 


Zo/.s-ora 


?n  > 


jyzj- 


/Zfy^iZ 


/  o/sc\ 
?  /  ?  f  > 


yttja 


U 


CiyxiA^z 


442  PRACTICAL  BUSINESS   ARITHMETIC 

4.  Jan.  1,  1916,  C.  H.  Smith  and  W.  W.  Osgoodby  formed 
a  copartnership  for  the  purpose  of  carrying  on  a  real  estate 
business.  C.  H.  Smith  invested  §15,000  and  W.  W.  Osgoodby 
$10,000.  They  agreed  to  share  the  gains  and  losses  in  pro- 
portion to  the  average  net  investment.  July  1,  1915,  C.  H. 
Smith  withdrew  ilOOO  and  W.  W.  Osgoodby  $750.  On  clos- 
ing the  books  at  the  end  of  the  year  the  net  gain  was  found  to 
be  $8685.  What  was  each  partner's  present  worth  after  his 
account  was  credited  with  his  share  of  the  net  gain  ? 

5.  Frank  M.  Congdon,  E.  H.  Robinson,  and  O.  B.  Moulton 
are  partners  in  a  dry  goods  house  under  the  firm  name  of 
E.  H.  Robinson  &  Co.  On  commencing  business  Aug.  1, 1916, 
Frank  M.  Congdon  invested  $17,500,  E.  H.  Robinson  $20,000, 
and  O.  B.  Moulton  $12,000.  The  articles  of  agreement  pro- 
vided ;  (1)  that  each  partner  should  be  allowed  interest  at  6% 
on  investments  and  charged  interest  at  the  same  rate  on  with- 
drawals; (2)  that  because  of  special  skill  and  experience 
Frank  M.  Congdon  should  be  credited  $1500  before  any  other 
division  of  the  gains  and  losses  ;  (3)  that  then  the  gains  should 
be  divided  equally.  Aug.  1,  1917,  the  results  of  the  year's 
business  were  as  follows  :  cost  of  merchandise  purchased, 
$80,872;  value  of  merchandise  on  hand,  $1-1,280.95;  sales  of 
merchandise,  $78,756;  cost  of  real  estate,  $18,000;  cost  of 
permanent  improvements  on  real  estate,  $1200;  present  esti- 
mated value  of  real  estate,  $  25,000 ;  notes  in  favor  of  the  firm, 
$11,500;  interest  accrued  on  these  notes,  $112;  cost  and  pres- 
ent value  of  horses  and  wagons,  $  1250 ;  general  expenses  for 
the  year  (exclusive  of  the  amount  due  Congdon),  $1800  ;  trav- 
eling expenses  for  the  year,  $1200;  accounts  owing  the  firm, 
$20,160.90;  cash  on  hand,  $19,033.10 ;  mortgage  on  the  firm's 
real  estate,  $12,000;  interest  accrued  on  the  mortgage,  $480; 
notes  outstanding,  $3500;  accounts  owed  by  the  firm,  $11,260. 
Show  in  proper  statements  the  financial  condition  of  the 
partners. 


CHAPTER   XXXVI 

STORAGE 
SIMPLE   STORAGE 

ORAL  EXERCISE 

1.  I  stored  my  piano  in  a  warehouse  from  June  16  to  Octo- 
ber 1  at  il  per  month  or  fraction  thereof.  What  sum  must  I 
pay  in  settlement  ? 

2.  I  rented  a  room  in  a  storage  warehouse  from  Sept.  1  to 
Dec.  18  at  16.50  per  month  or  fraction  thereof.  What  amount 
did  I  have  to  pay  ? 

3.  What  must  I  pay  for  tlie  storage  of  5000  bu.  of  wheat 
stored  from  Dec.  3  to  Apr.  15  at  4^  per  bushel  per  month  or 
fraction  thereof  ?  for  the  storage  of  10,000  bu.  of  corn  stored 
from  Dec.  1  to  Mar.  1  at  3|^  per  bushel  per  month? 

521.  Storage  is  a  charge  made  for  storing  goods  in  a  ware- 
house. 

522.  The  term  of  storage  is  the  period  of  time  for  which  a 
certain  rate  is  charged. 

The  term  of  storage  is  usually,  though  not  invariably,  30  da. ;  and  in 
estimating  charges,  a  part  of  a  term  is  counted  the  same  as  a  full  term. 

523.  The  rates  of  storage  are  sometimes  fixed  by  an  agree- 
ment between  the  contracting  parties,  sometimes  by  boards  of 
trade,  chambers  of  commerce,  or  associations  of  warehousemen, 
and  sometimes  by  legislative  enactment. 

524.  Simple  storage  is  storage  estimated  at  the  time  of  the 
withdrawal  of  the  goods  from  the  warehouse. 

443 


444 


PRACTICAL   BUSINESS   ARITHMETIC 


ORAL  EXERCISE 

1.    Verify  the  following  storage  bill: 


yi^^^a/SlA/^r^yf^^^^ 


To  Qiiincy  Market  Cold  Storage  and  Warehouse  Co.,  Dr. 

Main  Office,  133  Commercial  Street 
FOR    STORAGE 


DATE 
RECEIVED 


MERCHANDISE 


ZJA 


A^i?/?-^^. 


TZta^zA 


^^. 


^ 


A^ 


JX- 


^ 


7^ 


/j^a 


^ysr^.^ 


/■-n? 


£^ 


% 


IMi 


diA 


2.  When  were  the  eggs  received  for  storage  ?  If  there  are 
30  doz.  in  a  case,  how  many  dozen  were  received  ? 

3.  Suppose  the  rate  in  the  bill  were  10^  per  case  per  month 
or  fraction  thereof  for  the  first  3  mo.,  and  bf  per  case  per 
month  after  the  first  3  mo.  What  would  this  rate  be  for  4  mo.  ? 
for  7  mo.  ?    for  9  mo.  ?    for  10  mo.  ?    for  11  mo.  ? 

4.  Using  the  rate  in  the  bill,  find  the  storage  on  150  cs.  eggs 
stored  from  July  1  to  Jan.  14  ;  on  500  cs.  eggs  stored  from 
July  3  to  June  14;  on  350  cs.  eggs  stored  from  June  14  to 
Mar.  4  ;  on  12,000  doz.  eggs  stored  from  June  14  to  Nov.  18. 

5.  The  storage  rate  on  poultry  is  ^  ^  per  pound  per  month. 
Find  the  storage  on  1000  lb.  from  Jan.  10  to  Feb.  6  ;  on  800 
lb.  from  Jan.  10  to  Feb.  18  ;  on  1200  lb.  from  Jan.  10  to  May 
27  ;  on  1600  lb.  from  Jan.  10  to  July  3. 

6.  In  a  certain  warehouse  the  rate  of  storage  on  cheese  is  8  ^ 
per  100  lb.,  for  each  month  or  fraction  thereof.  At  that  rate 
find  the  storage  on  1000  lb.  cheese  from  May  3  to  July  15 ;  on 
20,000  lb.  from  May  3  to  Aug.  26  ;  on  7500  lb.  from  May  3  to 
Sept.  12 ;  on  10,000  lb.  from  May  3  to  Oct.  6  ;  on  5  T.  from 
June  15  to  Oct.  28 :  on  10  T.  from  June  15  to  Nov.  17. 


STORAGE 


445 


525.  Example.  The  following  memorandum  of  flour  stored 
for  you  by  the  Central  Storage  Co.  :  received  Nov.  1,  2000  bbl., 
and  Nov.  16,  3000  bbl. ;  delivered  Nov.  8, 1000  bbl.,  and  Dec.  5, 
4000  bbl.  If  the  rate  of  storage  was  b^  per  barrel  per  month 
or  fraction  thereof,  what  was  the  bill  to  render  ? 


7  da. 


Solution 
Receipts  and  Deliveries 
Nov.    1,  received  2000  bbl. 
Nov.    8,  delivered  1000  bbl. ,  which  were  in  storage 

1000  bbl.,  balance  in  storage 
Nov.  16,  received  3000  bbl. 

4000  bbl.,  balance  in  storage 
Dec.  5,  delivered  4000  bbl.,  1000  of  which  were  in  storage  34  da 
3000  of  which  were  in  storage  19  da. 
Total  storage. 


Term  Rate 'Storage 


10; 


$50 


100 

150 
$300 


WRITTEN  EXERCISE 

1.  In  a  certain  warehouse  the  storage  charges  on  flour  are  3  ^ 
per  barrel  per  month  or  fraction  thereof.  Nov.  1,  I  stored  500 
bbl. ;  Dec.  1,  I  withdrew  100  bbl.  ;  Jan.  1,  I  stored  600  bbl. ; 
Mar.  1,  I  withdrew  1000  bbl.  What  was  the  storage  on  the  first 
withdrawal  ?  400  bbl.  of  the  second  withdrawal  was  in  storage 
for  how  many  months  ?     What  was  the  total  storage  due  Mar.  1  ? 

2.  How  much  is  due  on  the  following  account? 


Received  from. 


Article   ^~-:^^^^^/^^, 


SR.oofi 


-hkt. 


zy  1,^ 


r 


Jb. 


Weight J~A^C^^ 


Sec  finn        ^/—  ■ 


State -jLc^T^^ll' 


Jb. 


DELIVERIES  AND  CHARGES 


^^^ 


2^z^ 


^ 


ji. 


ZjL 


^L- 


2a- 


^fLj^ 


/J^Zj2±  ^^ 


'Ud- 


:/u 


/M2/Z^ 


Jl 


'^na^ 


d£. 


446 


PRACTICAL   BUSINESS   ARITHMETIC 


3.  The  following  is  a  memorandum  of  apples  stored  by  you 
for  T.  B.  Welch  &  Co.  :  received  Nov.  28,  5000  bbl.,  Dec.  15, 
1000  bbl.,  and  Dec.  18,  3000  bbl.;  delivered  Dec.  28,2000  bbl., 
Feb.  1,  1000  bbl.,  and  Feb.  10,  6000  bbl.  Render  a  bill  for 
the  storage,  charges  being  5^  per  barrel  per  month  or  fraction 
thereof. 

4.  Copy  and  complete  the  following  bill : 


\IL^£^A^£^L^ 


J- 


z^<^  /^Srw^^:z^;^^^-4-^4^ 


To  EASTERN  COLD  STORAGE  CO.,  Dr. 

28  to  44  North  Street 

FOR  STORAGE 


?^ 


//g/7    /' 


JO/7/?^       vjT^/ 


^2E^^ 


Lm. 


'y.fi^OTf     fc 


-A 


Uy>7J  ..  ? 


dZ 


ATr?     /., 


/./gW       ft?^ 


AVERAGE   STORAGE 


526.  When  there  are  frequent  receipts  and  deliveries  of 
goods,  it  is  customary  for  some  warehouses  to  average  the  time 
and  charge  a  certain  rate  per  month  of  thirty  days.  The 
process  is  called  average  storage. 

527.  Example.  The  following  is  a  memorandum  of  the  re- 
ceipts and  deliveries  of  flour  stored  by  the  Eastern  Storage  Co. 
for  A.  M.  Briggs  &  Co. :  received  Apr.  10,  2000  bbl.,  and  Apr. 
30,  3000  bbl.;  delivered  May  8,  1000  bbl.,  and  June  9,  4000  bbl. 
The  storage  charge  being  41  ^  per  barrel  per  term  of  30  da. 
average  storage,  what  was  the  amount  of  the  bill  to  render  ? 

Solution.  The  solution  of  this  problem  is  clearly  shown  in  the  following 
statement  of  account : 


STORAGE 


447 


Account  of  Flour  Received  and  Delivered  by 

EASTERN   STORAGE   CO. 

For    A.    M.    BRIGGS    &    CO. 


Time  m 

Quantity  in 

Date 

Receipts 

Deliveries 

Balance 

Storage 

Storage  for  1  da. 

19- 

Apr. 

10 

2000  bbl. 

2000  bbl. 

20  da. 

40000  bbl. 

30 

3000  bbl. 

5000  bbl. 

8  da. 

40000  bbl. 

May 

8 

1000  bbl. 

4000  bbl. 

32  da. 

128000  bbl. 

June 

9 

4000  bbl. 

0000  bbl. 

00  da. 

00000  bbl. 

5000  bbl. 

5000  bbl. 

30)208000  bbl. 

Average  storage  for  1  mo.  =  6933^  bbl. 


69331  bbl.  dit4k\f  —  $312,  the  amount  of  the  bill  to  render. 


WRITTEN  EXERCISE 

1.  The  Quincy  Storage  and  Warehouse  Co.  received  and 
delivered  on  account  of  Boynton  Travers  &  Co.  sundry  barrels 
of  apples  as  follows  :  received  Dec.  1,  1915,  1000  bbl.,  Dec.  26, 
2000  bbl.;  delivered  Feb.  1,  500  bbl..  Mar.  1,  1000  bbl.. 
Mar.  15,  1100  bbl..  Mar.  31,  400  bbl.  If  the  charges  were 
6^  per  barrel  per  term  of  30  da.  average  storage,  what  was 
the  amount  of  the  bill  to  render? 

2.  The  Central  Storage  Warehouse  Co.  received  and  delivered 
on  account  of  A.  S.  Osborn  &  Co.  sundry  bushels  of  wheat  as 
follows  :  received  Oct.  1, 17,600  bu.,  Nov.  15,  3600  bu.,  Dec.  18, 
4200  bu.,  Dec.  27,  4320  bu.;  delivered  Oct.  31,  10,000  bu., 
Dec.  4,  10,720  bu.,  Dec.  19,  4000  bu.,  Dec.  28,  5000  bu.  If 
the  charges  were  T|  ^  per  bushel  per  term  of  30  da.  average 
storage,  what  was  the  amount  of  the  bill  to  render  ? 

3.  Metropolitan  Storage  Co.  received  and  delivered  on  ac- 
count of  Chas.  B.  Sherman  sundry  barrels  of  flour  as  follows : 
received  Nov.  15,  1915,  1800  bbl.,  Nov.  30,  1000  bbl.,  Dec.  18, 
600  bbl.,  Jan.  30,  3000  bbl.  ;  delivered  Dec.  1,  1000  bbl., 
Dec.  31,  1900  bbl.,  Jan.  31,  600  bbl.,  Feb.  5,  600  bbl.,  Apr.  30, 
2300  bbl.  If  the  charges  were  5J^per  barrel  per  term  of  30 
da.  average  storage,  what  was  the  amount  of  the  bill  to  render  ? 


448  PRACTICAL  BUSINESS  ARITHMETIC 

WRITTEN    REVIEW   EXERCISES 

1.  I  bought  wheat  at  $0.80  per  bushel  and  put  it  in  storage. 
If  the  storage  charges  were  2%,  for  how  much  must  I  sell  the 
wheat  to  realize  a  gain  of  $0.12  per  bushel,  and  make  allowance 
of  6  %  for  incidentals  ? 

2.  A  produce  dealer  bought  150  T.  cabbage-at  $  5.50  per  ton.- 
He  paid  90  ^  per  ton  for  storage  and  then  sold  the  cabbage  at  a 
clear  profit  of  25%.  How  much  did  he  receive  per  ton  and 
what  was  his  gain  ? 

3.  Nov.  1  a  speculator  bought  5000  bbl.  apples  at  $2.25  per 
barrel  and  put  them  in  storage.  Feb.  1  he  withdrew  them 
from  the  storage  warehouse.  He  had  them  sorted  and  repacked, 
when  he  found  that  he  had  only  4600  bbl.  of  sound  apples. 
These  he  sold  at  $3.50  per  barrel.  If  the  storage  charges 
were  5^  per  barrel  per  month  or  fraction  thereof,  and  the 
charges  for  repacking  were  $500,  did  he  gain  or  lose,  and  how 
much  ?  what  per  cent  ? 

4.  Dec.  15,  1915,  A.  L.  Farley  bought  1000  bbl.  flour  at 
$4  and  placed  it  with  the  Union  Warehouse  Co.  for  storage. 
Jan.  15  he  bought  3000  bbl.  flour  at  $4.15  and  placed  it  with 
the  same  warehouse  company  for  storage.  On  Feb.  15  he  with- 
drew 2000  bbl.  from  storage  and  sold  it  at  $5.85,  on  Mar.  25 
he  withdrew  1000  bbl.  and  sold  it  at  $  5.62^,  on  Apr.  1  he  with- 
drew 1000  bbl.  and  sold  it  at  $  5. 87 J.  If  the  storage  charges 
were  5^  per  barrel  per  month  or  fraction  thereof,  and  cartage 
and  incidentals  cost  $  100,  did  he  gain  or  lose,  and  how  much  ? 


APPENDIX   A 


ADDING   MACHINES 


Machines  or  mechanical  devices  for  performing  arithmetical  calculations  are 
now  commonly  used  in  business  offices ;  in  banks,  factories,  insurance  offices, 
and  wholesale  and  retail  houses  they  may  be 
regarded  as  indispensable. 

A  machine  will  list  and  add  figures  in  one 
fifth  or  one  sixth  of  the  time  in  which  the 
work  can  be  done  by  a  person  using  a 
pen  or  a  pencil,  and  with  an  accuracy 
that  a  person  cannot  equal.    The 
operations  of  subtraction,  multi- 
plication,   division,    and    trade 
discount  may  be  as  readily  per- 
formed as  those  in  addition. 

The   machine  writes  figures 
as  rapidly  as  a  typewriter,  and 
as  legibly ;  figures  are  recorded 
by   simply   touching  the   keys. 
The   figures  written   down   are 
added  automatically,  and  at  any 
time,  by  the  mere  operation  of  a 
handle,  will  be  recorded  without 
the  possibility  of  an  error,  the 
absolutely  correct  total.     When 
an   item  is  incorrectly  put 
into  the  keyboard,  it  may, 
before  pulling  the  handle,  be 
corrected. 

Machines  are  of 
different  sizes,  and 
some  machines  have 
paper  carriages  simi- 
lar to  the  carriage 
on  a  typewriter ;  on 
these    carriages,    if 
desired,  results  are 
printed  and  carbon 
copies  made.     Ma- 
chines   may    be 
furnished     with 
an  electric  drive, 
thus  avoiding  the 
handle  pull. 

449 


450 


PKACTICAL   BUSINESS  AEITHMETIC 


Machines  can  be  equipped  for  adding  dollars  and  cents ;  feet  and  inches  • 
dozens  and  gross ;  hours  and  minutes ;  tons  and  hundred  weights ;  pounds  and 

bushels;      grains     and     penny- 
weights;   English   pounds,   shil- 
lings, and  pence,  or  any  other 
kind  of  foreign  money ;  dates  and 
amounts ;  or  any  kind  of  figures. 
Machines    may    be    equipped 
with  the   unlimited  split  device 
for  dividing  the  keyboard  into 
two  or  more  sections,  for  listing 
and  adding  two  or  more  sets  of 
figures  at  one  operation.     Thus 
they  may  also  be  equipped  with 
devices  for  automatically  listing 
and  adding  across  the  sheet  or 
form  in  two  or  more  columns. 
There  is  a  duplex  adding  machine 
with  two  sets  of  wheels,  to  accumulate  two 
separate  totals  at  the  same  time.  With  a  ma- 
chine of  this  type,  totals  of  groups  of  items 
may  be  secured  and  a  grand  total  of  the 
group  totals  accumulated  at  the  same  time. 
Adding-subtracting  machines  add  debits, 
subtract  credits,  and  automatically  compute 
the  difference  and  print  it.  There  are  special 
"^^^  adding   machines    for    handling   monthly 

statements  and  for  ledger  posting  and  cost 
accounting ;  a  pay-roll  machine  that,  with  one  operation,  prints  the  employees' 
numbers  and  the  amount  of  pay  on  the  pay-roll  sheet  and  pay  envelopes. 

The  following  are  some  of  the  uses  of  these 
machines  in  offices :  proving  daily  postings ;  daily 
ledger  balance  ;  daily  cash  balance ;  daily  reca- 
pitulation of  sales  (as  cash,  credit,  C.O.D.,  etc.] 
checking   invoices    and   freight   bills;    figuring 
discounts;    computing   commissions;    summary 
of  day's  receipts  and  disbursements;   figuring 
estimates;   making  out  pay  envelopes; 
analysis  of  outstanding  accounts ;  analy- 
sis of  accounts  payable ;  balancing  petty 
cash  account;   footing  ledger  accounts 
before  taking  the  trial  balance ;  taking 
off  the  trial-balance  figures  (debits  and 
credits) ;   reconciling  caslibook  balance 
with  bank  balance,  listing  the  number 
and  the  amount  of   each   outstanding 
check ;  making  monthly  statements  giv- 
ing month,  date,  total  of  debits,  total  of 
credits,  balance  and  special  terms ;  compiling  statements  of  cost  of  production ; 
footing  inventories  and  calculating  extensions ;  posting  customers'  Jedger. 
The  cuts  show  various  types  of  calculating  machines. 


APPENDIX   B 
TABLES   OF   MEASURES 

MEASURES  OF  CAPACITY 

Liquid  Measure  Dry  Measure 

4  gills     =  1  pint  2  pints    =  1  quart 

2  pints    =  1  quart  8  quarts  =  1  peck 

4  quarts  =  1  gallon  4  pecks  =  1  bushel 

=  231  cubic  inches  =  215D.42  cubic  inches 

Barrels  and  hogsheads  vary  in  size  ;  but  in  estimating  the  capacity  of  tanks 
and  cisterns  31.5  gal.  are  considered  a  barrel,  and  2  bbl.,  or  63  gal.,  a  hogshead. 

A  heaped  bushel,  used  for  measuring  apples,  corn  in  the  ear,  etc.,  equals 
2747.71  cu.  in.  A  dry  quart  equals  67.2  cu.  in.,  and  a  liquid  quart  57.75 
cu.  in. 

MEASURES  OF  WEIGHT 

Avoirdupois  Weight  Troy  Weight 

16*  ounces  =  1  pound  24  grains  =  1  pennyweight 

100  pounds  =  1  hundredweight  20  pennyweights  =  1  ounce 

2000  pounds  =  1  ton  12  ounces  =  1  pound 

Apothecaries'  Weight  Comparative  Weights 

20  grains     =  1  scruple  1  lb.  troy  or  apothecaries'  =  5760  gr. 

3  scruples  =  1  dram  1  oz.  troy  or  apothecaries'  =    480  gr. 

8  drams     =  1  ounce  1  lb.  avoirdupois  =  7000  gr. 

12  ounces    =  1  pound  1  oz.  avoirdupois  =  437^  gr. 

The  ton  of  2000  lb.  is  sometimes  called  a  short  ton.  There  is  a  ton  of  2240  lb., 
called  a  long  ton,  used  in  all  customhouse  business  and  in  some  wholesale  trans- 
actions in  mining  products. 

In  weighing  diamonds,  pearls,  and  other  jewels,  the  unit  generally  employed 
is  the  carat,  equal  to  3.2  troy  grains.  The  term  "  carat"  is  also  used  to  express 
the  number  of  parts  in  24  that  are  pure  gold.  Thus,  gold  that  is  14  carats  fine 
is  II  pure  gold  and  \%  alloy. 

Miscellaneous  Weights 

1  keg  of  nails       =100  pounds  1  barrel  of  salt  =  280  pounds 

1  cental  of  grain  =  100  pounds  1  barrel  of  flour  =196  pounds 

1  quintal  of  fish  =  100  pounds  1  barrel  of  pork  or  beef  =  200  pounds 

A  cubic  foot  of  water  contains  about  7i  gal.  and  weighs  62 1  lb.,  avoirdupois. 

451 


452 


PRACTICAL   BUSINESS   ARITHMETIC 


MEASURES  OF  EXTENSION 


Long  Measure 


12  inches  =  1  foot 

3  feet  =  1  yard 

5|  yards,  or  16 1  feet  =  1  rod 
320  rods,  or  5280  feet  =  1  mile 


Surveyors*  Long  Measure 

7.92  inches  =  1  link 

25  links  =  1  rod 

4  rods,  or  100  links  =  1  chain 
80  chains  =  1  mile 


City  lots  are  usually  measured  by  feet  and  decimal  fractions  of  a  foot ;  farms, 
by  rods  or  chains. 


Miscellaneous  Long  Measures 

4  inches  =  1  hand 

6  feet  =  1  fathom 

120  fathoms        •  =  1  cable  length 
1.15  miles,  nearly,  =  1  knot,  or 
1  nautical  or  geographical  mile 


Square  Measure 

144  square  inches  =  1  square  foot 
9  square  feet      =  1  square  yard 
30|  square  yards  =  1  square  rod 
160  square  rods      =  1  acre 
640  acres  =  1  square  mile 


The  hand  is  used  in  measuring  the  height  of  horses  at  the  shoulder.  The 
fathom  and  cable  length  are  used  by  sailors  for  measuring  depths  at  sea.  The 
knot  is  used  by  sailors  in  measuring  distances  at  sea.  Tliree  knots  are  frequently 
called  a  league. 


Surveyors*  Square  Measure 

625  square  links    =  1  square  rod 
16  square  rods      =  1  square  chain 
10  square  chains  =  1  acre 

640  acres  =  1  square  mile 

36  square  miles   =  1  township 


Cubic  Measure 

1728  cubic  inches  =  1  cubic  foot 
27  cubic  feet     =  1  cubic  yard 
128  cubic  feet      =  1  cord 

1  cubic  yard    =  1  load  (of  earth,  etc.) 
24 1  cubic  feet     =  1  perch 


The  square  rod  is  sometimes  called  a  perch.  The  word  rood  is  sometimes 
used  to  mean  40  sq.  rd.  or  \  A.  In  the  government  surveys,  1  sq.  mi.  is  called 
a  section. 

The  perch  of  stone  or  masonry  varies  in  different  parts  of  the  country  ;  but 
it  is  usually  considered  as  1  rd.  long,  1  ft.  high,  and  li  ft.  thick,  or  24f  cu.  ft. 


Angular  Measure 


60  seconds  =  1  minute 
60  minutes  =  1  degree 


90  degrees  =  1  right  angle 
360  degrees  =  1  circumference 


Angular  (also  called  circular)  measure  is  used  principally  in  surveying,  navi- 
gation, and  geography  for  measuring  arcs  of  angles,  for  reckoning  latitude  and 
longitude,  for  determining  locations  of  places  and  vessels,  and  for  computing 
difference  of  time. 

A  minute  of  the  earth's  circumference  is  equal  to  a  geographieal  mile.  A 
degree  of  the  earth's  circumference  at  the  equator  is  therefore  equal  to  about 
69  statute  miles. 


TABLES  OF   MEASURES  453 

MEASURES  OF  TIME 

60  seconds  =  1  minute  12  months  =  1  year 

60  minutes  =  1  hour  360  days       =  1  commercial  year 

24  hours       =  1  day  365  days       =  1  common  year 

7    days        =  1  week  366  days       =  1  leap  year 

30  days        =  1  commercial  month  100  years      =  1  century 

September,  April,  June,  and  November  have  30  da.  each  ;  all  of  the  other 
months  have  31  da.  each,  except  February,  which  has  28  da.  in  a  common  year 
and  29  da.  in  a  leap  year. 

Centennial  years  that  are  divisible  by  400  and  other  years  that  are  divisible 
by  4  are  leap  years. 

In  running  trains  across  such  a  broad  stretch  of  country  as  the  United  States, 
it  is  highly  important  to  have  a  uniform  time  over  considerable  territory.  Rec- 
ognizing this,  in  1883,  the  railroad  companies  of  the  United  States  and  Canada 
adopted  for  their  own  convenience  a  system  of  standard  time.  This  System 
divides  the  United  States  into  four  time  belts,  each  covering  approximately  15'' 
of  longitude,  7^°  of  which  are  east  and  7^°  west  of  the  governing  meridian.  The 
.region  of  eastern  time  lies  approximately  7|°  each  side  of  the  75th  meridian, 
and  the  time  throughout  this  belt  is  the  same  as  the  local  time  of  the  75th  merid- 
ian. Similarly,  the  regions  of  central,  mountain,  and  Pacific  time  lie  approxi- 
mately 7|°  each  side  of  the  90th,  105th,  and  120th  meridians,  respectively,  and 
the  time  throughout  each  belt  is  determined  by  the  local  time  of  the  governing 
meridian  of  that  belt.  There  is  just  one  hour's  difference  between  adjacent  time 
belts.  Thus,  when  it  is  11  o'clock  a.m.  by  eastern  time,  it  is  10  o'clock  a.m.  by 
central  time,  9  o'clock  a.m.  by  mountain  time,  and  8  o'clock  a.m.  by  Pacific  time. 
Since  railroad  companies  change  the  time  at  important  stations  and  termini, 
regardless  of  the  longitude  of  such  stations  and  termini,  the  boundaries  of  the 
time  belts  are  quite  irregular. 

MEASURES  OF  VALUE 

United  States  Money  English  Money 

10  mills     =  1  cent  4  farthings  =  1  penny 

10  cents     =  1  dime  12  pence        =  1  shilling 

10  dimes    =  1  dollar  20  shillings  —  1  pound  sterling 
10  dollars  =  1  eagle  =  $4.8665 

The  term  "  eagle  "  is  seldom  used  in  business.  The  mill  is  not  a  coin,  but  the 
name  is  frequently  used  in  some  calculations.  In  Canada  the  units  of  money 
are  the  same  as  in  the  United  States.     1  far.  =  |Q^  ;  \d.  =  2,^-^^  ;  Is.  =  '2.^\f. 

French  Money  German  Money 

100  centimes  =  1  franc  =  $0,193  100  pfennigs  =  1  mark  =  $0,238 

MISCELLANEOUS  MEASURES 

Counting  by  12  Counting  Sheets  of  Paper 

12  things  =  1  dozen  24  sheets  =  1  quire 

12  dozen    =  1  gross  20  quires  =  1  ream 
12  gross     =  1  great  gross  =  480  sheets 


454 


PEACTICAL   BUSINESS   ARITHMETIC 


BUSINESS   ABBREVIATIONS 


A  . 

.     .  acre 

Mar.   . 

.     .  March 

Apr. 

.  April 

Mdse. 

.     .  merchandise 

Aug. 

.  August 

Messrs. 

.     .  Messieurs,    Gentlemen ; 

bbl. 

.  barrel;  barrels 

Sirs 

bdl. 

.     .  bundle;  bundles 

mi.     . 

.     .  mile;  miles 

bg. 

.  bag;  bags 

min.  . 

.     .  minute;  minutes 

bkt. 

.  basket;  baskets 

mo.     . 

.     .  month;  months 

bl. 

.     .  bale;  bales 

Mr.     . 

.     .  Mister 

bu. 

.  bushel;  bushels 

Mrs.   . 

.     .  JMistress 

bx. 

.     .  box;  boxes 

N.'     . 

.     .  north 

cd. 

.     .  cord;  cords 

No.     . 

.     .  number 

ch. 

.     .  chain ;  chains 

Nov.  . 

.     .  November 

c.i.f. 

.     .  carriage  and  insurance  free 

Oct.    . 

.     .  October 

Co. 

.  company;  county 

oz. 

.     .  ounce;  ounces 

C.O.D 

.    .  collect  on  delivery 

p.  .     . 

.     .  page 

Coll. 

.  collection 

pc.       . 

.     .  j)iece;  pieces 

Cr. 

.  creditor;  credit 

per.     . 

.     .  by  the  ;  by 

cs. 

.     .  case ;  cases 

per  cent. 

.  per  centum,  by  the  hun- 

ct. 

.  cent ;  cents ;  centime 

dred 

cu.  ft. 

.  cubic  foot ;  cubic  feet 

pk.      . 

.     .  peck  ;  pecks 

cu.  in. 

.  cubic  inch ;  cubic  inches 

pkg.    . 

.     .  package ;  packages 

cu.  yd 

.     .  cubic  yard ;  cubic  yards 

pp.      . 

.     .  pages 

cwt. 

.     .  hundredweight 

pr.       . 

.     .  pair;  pairs 

d.  . 

.     .  pence 

pt.       . 

.     .  pint ;  pints 

da. 

.     .  day;  days 

pwt.    . 

.     .  pennyweight;      penny- 

Dec. 

.     .  December 

weights 

doz. 

.     .  dozen;  dozens 

qr.       . 

.     .  quire;  quires 

Dr. 

.     .  debtor  ;  debit ;  doctor 

qt.       . 

.     .  quart;  quarts 

E.  . 

.     .  east 

rd.       . 

.     .  rod  ;  rods 

ea. 

.     .  each 

rm.      . 

.     .  ream  ;  reams 

e.g. 

.     .  exempli    gratia,      for    ex- 

Km. (or 

VI.)   Reichsmark,  Mark 

ample 

s.    .     . 

.     .  shilling;  shillings 

etc. 

.     .  et  ccetera,  and  so  forth 

S.  .     . 

.     .  South 

far. 

.     .  farthing;  farthings 

sec.     . 

.     .  second;  seconds 

Feb. 

.     .  February 

sq.  ch. 

.     .  square     chain;     square 

f.o.b. 

.     .  free  on  board 

chains 

fr. 

.     .  franc ;  f i-ancs 

sq.  ft. 

.     .  square  foot ;  square  feet 

ft. 

.     .  foot;  feet 

sq.  mi. 

.     .  square      mile;      square 

gal. 

.     .  gallon;  gallons 

miles 

gi- 

•     •  gill;  gills 

sq.  rd. 

.     .  square  rod ;  square  rods 

gr. 

.     .  grain  ;  grains 

sq.  yd. 

.     .  square     yard;      square 

gro. 

.     .  gross 

yards 

hhd. 

.     .  hogshead;  hogsheads 

T.  .    . 

.     .  ton 

hf.  ch 

t.    .  half  chest ;  half  chests 

tb.      . 

.     .  tub;  tubs 

hr. 

.     .  hour  ;  hours 

Tp.     . 

.     .  township  ;  townships 

i.e. 

.     .  id  est,  that  is 

viz. 

.     .  videlicet,  namely ;  to  wit 

in. 

.     .  inch;   inches 

via 

.     .  by  way  of 

Jan. 

.     .  January 

wk.     . 

.     .  week;  weeks 

kg. 

.     .  keg  ;  kegs 

wt.      . 

.     .  weight;  weigh 

1.    . 

.     .  link  ;  links 

yd.      . 

.     .  yard;  yards 

lb. 

.     .  pound;  pounds 

yr-    • 

.     .  year ;  years. 

BUSINESS   SYMBOLS  AND  ABBREVIATIONS      455 


BUSINESS   SYMBOLS 


«/c 

account 

■=. 

equal;  equals 

13 

one  and  three 

«A 

account  sales 

foot;  feet; 

fourths 

+ 

addition 

minutes 

^ 

per;  by 

or 

~~  aggregation 

C 

hundred 

% 

per  cent ; 

& 

and 

II 

inch  ;  inches  ;  seconds 

hundredth ; 

. . .  • 

.   and  so  on 

X 

multiplication 

hundredths 

@ 

at;  to 

# 

number,  if  written 

£ 

pounds  sterling 

'/o 

care  of 

before  a  figure; 

•/ 

since 

f 

cent;  cents 

pounds,  if  written 

— 

subtraction 

V 

check  mai'k 

after  a  figure 

therefore 

o 

degree 

11 

one  and  one  fourth 

M 

thousand 

^ 

division 

12 

one  and  two  fourths ; 

V6 

5  shillings  6  pence  ; 

1 

dollar;  dollars 

one  and  one  hall 

five  sixths 

INDEX 


Abbreviations,  454 

Above  par,  398 

Abstract  number,  50 

Account,  41 

Account  current,  415,  417 

Account  purchase,  271,  275 

Account  sales,  271,  392 

Acute  angle,  201 

Acute-angled  triangle,  202 

Adding  machines,  449 

Addition,  10,  94,  125,  194 

Ad  valorem  duty,  291,  295 

Agent,  270 

Aliquot  parts,  158 

Altitude,  204 

Amount,  232,  328 

Angle,  201 

Angular  measure,  452 

Apothecaries'  weight,  451 

Arabic  numerals,  3 

Arc,  202 

Areas,  204 

Assessment,  397,  400 

At  a  discount,  366,  398 

At  par,  366 

At  a  premium,  366,  398 

Average,  85 

Average  clause,  284 

Average  date  of  payment,  385 

Average  investment,  438 

Average  storage,  446 

Average  term  of  credit,  385 

Avoirdupois  weight,  451 

Bank  discount,  326,  327 

Bank  drafts,  358,  360 

Bank  loans,  334 

Bank  money  order,  355 

Bankers'  bills  of  exchange,  375,  377 

Bankers'  daily  balances,  346 

Banker's  sixty-day  method  of  interest, 

303 
Banking,  300 
Base,  204,  232,  236 
Base  line,  205 
Bear,  416 
Below  par,  398 


Bill  of  lading,  366 

Bills,  39,  40,  59,  63,  106,  107,  134,  152, 
165,  166,  170,  171,  172,  173,  174,  175, 
176,  183,  187,  199,  248,  253,  254,  268, 
269,  297,  298 

Bills  and  accounts,  170 

Bills  of  exchange,  375,  378,  379 

Bins,  226 

Blank  indorsement,  315 

Blanket  policy,  278 

Board  foot,  220 

Bonds,  405,  406 

Bond  table,  409 

Brick  work,  225 

Broker,  270 

Brokerage,  270 

Bull,  416 

Bullion,  9 

Buying  bonds,  410 

Buying  on  commission,  274 

Buying  by  the  hundred,  105 

Buying  by  the  thousand,  105 

Buying  by  the  ton,  108 

Buying  stocks,  402 

Cable  length,  452 

Calculation  table,  229 

Cancellation,  115 

Capacity,  226 

Capital,  429 

Capital  stock,  396 

Capitation  tax,  286 

Carpeting,  215 

Cash  account,  41 

Cash  balance,  393 

Cashier's  check,  361 

Certificate  of  deposit,  361 

Change  memorandum,  181 

Charter,  396 

Checking  results,  20,  32,  52,  57,  58,  69, 

87,  88,  89 
Checks,  5,  358, 362,  383,  400 
Circle,  202 
Circumference,  202 
Cisterns,  224 
Clearing  house,  358,  359 
Code,  356 


457 


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460 


PRACTICAL  BUSINESS  ARITHMETIC 


Obtuse  angle,  201 
Obtuse-angled  triangle,  202 
Odd  number,  113 
One-fourth  pitch,  210 
One-half  pitch,  210 
Open  policy,  278 
Orders  of  units,  3 
Ordinary  life  policy,  420 
Ordinary  policy,  278 

Paid-up  policy,  421 
Painting,  213 
Papering,  216 
Par  value,  398 
Parcel  post,  77 
Parenthesis,  31 
Partial  payments,  338 
Partitive  proportion,  426 
Partners,  429 
Partnership,  429 
Pay  rolls,  86,  181,  182,  185 
Payee,  315,  327 
Pay-roll  memorandum,  182 
Per  cent,  92,  231 
Per  cents  of  decrease,  238 
Per  cents  of  increase,  237 
Percentage,  231 
Perch,  225,  452 
Perimeter,  202 
Periodic  interest,  319 
Periods,  4 

Perpendicular  lines,  201 
Personal  accounts,  42 
Pitch  of  roof,  210 
Place  value,  3 
Plane  surface,  201 
Plastering,  212 
Policy,  278 
Poll  tax,  286 
Port  of  delivery,  291 
Port  of  entry,  291 
Postal  money  order,  354 
Postal  savings  bank,  352 
Postal  service,  77 
Power,  51 

Practical  measurements,  201 
Preferred  stock,  397 
Premium,  278 
Present  worth,  41 
Prime  number,  113 
Principal,  270,  300 
Principal  meridian,  206 
Problems  in  interest,  318 
Proceeds,  328 

Promissory  notes,  9,  314,  316,  335,  336, 
341 


Properties  of  9,  87    • 
Properties  of  11,  88 
Property  insurance,  277- 
Property  tax,  286 
Proprietary  account,  43 
Public  lands,  205 

Qualified  indorsement,  316 
Quotient,  66 

Radical  sign,  '206 

Radius,  202 

Ranges,  205 

Rate,  232,  300 

Rate  of  exchange,  355,  360,  366,  376 

Reading  decimals,  92 

Rectangle,  201 

Rectangular  solids,  218 

Reduction,  121,  122,  123,  124,  192,  193 

Reference  method  of  interest,  313 

Registered  bond,  407 

Remainder,  66 

Repeaters,  264 

Reserve,  421 

Resource,  41 

Review  of  the  common  tables,  191 

Review  tests,  30,  49,  65,  112,  157,  245, 

255,  276,  337 
Right  angle,  201 
Right-angled  triangle,  202 
Roman  numerals,  6 
Rood,  452 


Savings  bank,  349 

Savings-bank  accounts,  349 

Scalene  triangle,  202 

Scrip,  399 

Section,  205 

Selling  on  commission,  272 

Selling^by  the  hundred,  105 

Selling  by  the  thousand,  105 

Selling  by  the  ton,  108 

Separatrix,  3 

Share,  396 

Shipment,  271 

Shipping  invoice,  273 

Short  methods,  55,  71,  126,  136 

Sight  draft,  364 

Similar  fractions,  124 

Simple  accounts,  385 

Simple  interest,  301 

Simple  storage,  443 

Sinking  fund,  323 

Six  per  cent  method  of  interest,  311 

Sixteen  to  one,  136 


INDEX 


461 


Solids,  218 

Solution  of  problems,  146 

Specific  duty,  291 

Square,  201,  209 

Square  measure,  452 

Square  root,  206 

Standard  time,  453 

Statements,  4^,  179,  180 

Statutory  weights  of  the  bushel,  200 

Stock  broker,  398 

Stock  certificates,  396,"  397,  398 

Stock  company,  396 

Stock  exchanges,  414 

Stock  insurance  company,  278 

Stockholder,  396 

Stocks  and  bonds,  396 

Stone  work,  225 

Storage,  443 

Stricken  bushel,  226 

Subtraction,  31,  96,  126,  194 

Surface,  201 

Surplus,  421 

Surveyors'  long  measure,  452 

Surveyors'  square  measure,  452 

Table  of  aliquot  parts,  160 
Table  of  bond  quotations,  410 
Table  of  common  measures,  451 
Table  of  compound  interest,  321,  323 
Table  of  foreign  coins,  293 
Table  of  important  per  cents,  232 
Table  of  insurance  rates,  281,  421 
Table  of  simple  interest,  314 
Table  of  stock  quotations,  402 
Table  of  time,  330 
Table  of  twelfths,  266 
Tables  of  metric  measures,  371 
Tare,  38 


Tariff,  291 

Tariff,  or  rate,  book,  281 

Tax  rate,  287 

Tax  table,  290 

Taxes,  286 

Telegram,  356 

Telegraphic  money  order,  356 

Telegraphic  rates,  357 

Term  of  discount,  328 

Term  of  storage,  443 

Term  policy,  420 

Terms  of  a  fraction,  120 

Tests  of  divisibility,  114 

Time  note,  315 

Time  sheets,  86,  181,  182,  185 

Time  slip,  185 

Township,  205 

Trade  discount,  246 

Traveler's  check,  381,  382 

Triangle,  202 

Troy  weight,  451 

Underwriter,  278 
Unit,  7 

Unit  fraction,  120 
United  States  coins,  8 
United  States  method  of  partial  pay- 
ment, 338 
United  States  money,  8,  9,  453 

Valued  policy,  278 

Values  of  foreign  coins,  293 

Vinculum,  31 

Warehousing,  293 
Warehouse  entry,  294 
Weigh  tickets,  108 
Wood,  220 


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ANSWERS  TO 

PRACTICAL  BUSINESS 
ARITHMETIC 


,1  BT 

\r)  JOHN  H.  MOOEE 


r 


AND 

\^^  GEOEGE  W.  MINEK 


^ 


REVISED  EDITION 


GINN  AND  COMPANY 

BOSTON  •  NEW  YORK  •  CHICAGO  •  LONDON 
COPYRIGHT,  1906,  1915,  BY  GINN  AND  COMPANY 


a 


A      ^    A    •- 


ANSWERS 

Page  4 

1.  6,006,005.  4.  321,000,006.  7.  27.125. 

2.  753,000,000,000.  5.  $3,000,004.05.  8.  62,000.425. 

3.  4,000,125.  6.  10,000,001,103.  9.  $3,420,001.15. 

Page  7 

1.  XIX  ;  LXXXVIII  ;  XCIX  ;  4.  MCDXCII,  or  MCCCCXCII ; 
CXXIV  ;  MCMVII ;  MCMX.  MDCXX  ;  MDCCLXXVI. 

2.985,100.  6.5,217,210,271.43; 
3.  5,217,210,000.016.  5,217,207,540.004. 

Page  19 

1.  19,857.      2.  16,665.       3.  11,028.      4.  30,316.       6.  24,396.      6.  9884. 

Page  20 
7.  45,842.     8.  25,895.     9.  25,317.     10.  17,599.     11.  29,839.     12.  17,007. 

Page  21 
1.  $1956.92.  2.  $16,326.51. 

Page  22 

1.  $37,358,013.62.  3.  $43,557,265.17.  6.  $9,264,451.21. 

2.  $36,243,941.97.  4.  $857,538.97.  6.  $11,603,633.30. 

Page  23 

7.  $6,312,125.73.  8.  $12,284,421.92.  9.  $19,813,964.89. 

Page  25 

1.  52.  4.  335.  7.  622.  10.  3221.  13.  $347.45. 

2.  67.  5.  572.  8.  488.  11.  4541.  14.  $732.48. 

3.  66.  6.  493.  9.  512.  12.  $357.39. 

RE        815.3  1 


2  PRACTICAL  BUSINESS  ARITHMETIC 

Page  26 

1.  212,400.  2.  74,784. 

3.  Vertical  totals:  pine,  $21,071.54  ;  oak,  $27,018.17  ;  maple,  $1794.21 ; 
spruce,  $1951.01;  walnut,  $2741.56;  cherry,  $1623.73.  Horizontal 
totals:  Monday,  $19,389.77;  Tuesday,  $9582.54;  Wednesday,  $10,620.78; 
Thursday,  $4351.68;  Friday,  $6454.51;  Saturday,  $5800.94.  Check, 
$56,200.22. 

Page  27 

4.  Horizontal  totals:  $77,591.59;  $156,846.01;  $70,092.38;  $4233.37; 
$74,992.38;  $102,960.37;  $17,848.77;  $14,610.08;  $5160.14;  $238,854.56; 
$18,660.82;  $10,869.85;  $114,162.44;  $18,604;  $2143.31.  Vertical  totals : 
$172,481.07;  $229,044.01;  $206,739.21;  $101,314.96;  $218,050.82.  Check, 
$927,630.07. 

6.  Horizontal  totals:  J.  E.  Snow,  $1192.67;  W.  B.  Moore,  $370.74; 
T.  B.  Welch,  $820.24 ;  E.  H.  Ross,  $1015.60 ;  Minnie  Davis,  $972.35  ; 
Ada  Benton,  $547.25;  Elmer  S.  Frey,  $3031.28;  Joseph  White,  $372.37; 
Margaret  Dix,  $304.55;  F.  O.  Beck,  $714.16;  L.  O.  Avery,  $1821.49; 
B.  W.  Snyder,  $848.11;  Ella  Harding,  $218.07 ;  Carrie  Simpson,  $222.53 ; 
W.  F.  Baldwin,  $827.65;  E.  O.  Burrill,  $772.05.  Vertical  totals:  Mon- 
day, $1859.95;  Tuesday,  $2647.98;  Wednesday,  $2931.92;  Thursday, 
$1997.10;  Friday,  $2447.18  ;  Saturday,  $2166.98.    Check,  $14,051.11. 

6.  a.  $13,785.29.    b.  $13,422.46.    c.  $13,365.10.    d.  $14,320.43. 


Page  29 

1.  52,187,258,800.  4.  47,498,388,917.  7.  47,480,394,697. 

2.  52,163,267,812.  6.  39,769,350,892.  8.  45,296,432,916. 

3.  55,583,217,175.  6.  51,571,866,229.  9.  46,907,836,534. 


Page  30 

1.  428,977 ;  422,257.  3.  Check,  12,496. 

2.  379,703  ;  445,056.  4.  Check,  11,079. 


Page  32 

1.  $60,766.18. 

BE 


ANSWERS  3 

Page  33 

2.  (a)  1904,  $1,460,827,271 ;  1905,  f  1,518,561,666  ;  1906,  |1, 743,864,500; 
1907,  $1,880,851,078;  1908,  |1,860,772,714 ;  1909,  $1,663,011,104;  1910, 
$1,744,984,720  ;  1911,  $2,049,320,199  ;  1912,  $2,204,322,409  ;  1913,  $2,465,- 
884,149.  (6)  1904,  $469,736,293  ;  1905,  $401,048,595  ;  1906,  $517,302,054  ; 
1907,  $446,429,653;  1908,  $666,430,922;  1909,  $351,090,880;  1910, 
$188,037,290;  1911,  $522,094,094  ;  1912,  $551,057,475  ;  1913,  $652,905,915. 
(c)  $18,592,399,810  ;  $13,826,266,639.  (d)  $4,766,133,171. 

Page  34 

1.  $317.         2.  $343.         3.  $274.         4.  $488. 

Page  35 

5.  $282.  6.  $361.  7.  Column  amounts :  $209.15;  $208.16;  $216.46. 
Line  amounts:  $720.42;  $506.18;  $661.42;  $508.28.  Check  total,  $2396.30. 

8.  a,  $721.12  ;  6,  $857.12  ;  c,  $717.75  ;  d,  $818.42  ;  e,  $419.37  ;/,  $374.20  ; 
g,  $3953.88  ;  h,  $41.51  ;  i,  $4.39  ;  j,  $3907.98. 

Page  38 

1.  a,  $1051  ;  &,  $942  ;  c,  $842  ;  d,  $918  ;  e,  $417  ;  /,  $830  ;  g,  $736  ; 
h,  $878 ;  i,  $833  ;  i,  $655  ;  k,  $934  ;  I,  $9050  ;  m,  $1942  ;  n,  $1928  ;  o,  $9036. 

2.  a,  $1021  ;  6,  $894 ;  c,  $871 ;  d,  $723 ;  e,  $591  ;  /,  $738 ;  g,  $759  ;  h,  $697 ; 
i,  $591  ;  j,  $922  ;  fc,  $1011  ;  I,  $7347  ;  m,  $2047  ;  n,  $3518  ;  o,  $8818. 

Page  39 

1.  $628.71. 

Page  40 

2.  $710.89.       3.  2163  lb.       4.  672  lb.        6.  3091  lb. 

Page  44 

1.  $1485.25,  balance.  3.  $205.55,  loss  ;  $255.55,  loss. 

2.  $72.06,  gain.  4.  $575.32,  liability. 

Page  45 

5.  $575.32,  balance.        6.  $7219.65,  present  worth. 

1.  Gain  on  mdse.,  $270.60  ;  cost  of  expense,  $478.60  ;  loss  on  expense, 
$78.60. 

2.  Total  resources,  $7212  ;  amount  owed  C.  H.  Jones,  $430.60;  present 
worth,  $5866.40. 

EE 


PRACTICAL  BUSINESS  ARITHMETIC 


3.  $4463.17. 

4.  $6189.25,  present  worth. 


Page  46 

5.  $728.35,  net  gain. 

6.  $3664.21,  net  gain. 


7.  $1346.50. 


Page  47 

Face  of  paper,  total  $2672.92 ;  2.  Face  of  paper,  total  $2339.82 ; 

Discount,  total  $19.84 ;         '  Discount,  total  $20.73; 

Collection  and  Exchange,  Collection  and  Exchange, 

total  $2.18;  total  $1.58; 

Proceeds,  total  $2650.90,  check.  Proceeds,  total  $2317.51,  check. 

3.  Face  of  paper,  total  $2118.31; 
Discount,  total  $13.90;     ' 
Collection  and  Exchange,  total  $1.79; 
Proceeds,  total  $2102.62,  check. 


Page 

1st  Balance,  total  $4353 ; 

Checks,  total  $4737; 

Deposits,  total  $2975 ; 

2d  Balance,  total  $2591,  check. 

1st  Balance,  total  $3331 ; 

Checks,  total  $3420 ; 

Deposits,  total  $2240 ; 

2d  Balance,  total  $2151,  check. 


48 
3. 


4. 


1st  Balance,  total  $3405 ; 

Checks,  total  $3684 ; 

Deposits,  total  $2347; 

2d  Balance,  total  $2068,  check. 

1st  Balance,  total  $3509 ; 

Checks,  total  $3684 ; 

Deposits,  total  $2233 ; 

2d  Balance,  total  $2058,  check. 


1st  column,  total  41,290; 
2d  column,  total  50,750; 
3d  column,  total  42,004 ; 
check,  134,044. 


3.  $4463.17. 


Page  49 

2.  1st  Balance,  total  $3541 ; 
Checks,  total  $2476 ; 
Deposits,  total  $2100 ; 
2d  Balance,  total  $3165,  check. 


4.  $3664.21. 


6.  $1346.50. 


1.  Check,  53,985. 


Page  53 

Check,  255,717. 


3.  Check,  $3186.60. 


4.  Check,  26,460. 

5.  Check,  911,204. 

6.  Check,  $1320.80. 


Page  54 

7.  $471.90. 

8.  $557.25,  gain. 

9.  $5.42. 


10.  $1867.48. 

11.  $182.13. 

12.  $1535.58. 


ANSWERS  5 

Page  57 

1.  $21,638.98. 

Page  58 
1.  $2213.87.  2.  $3141.40. 

Page  59 
3.  $90.15. 

Page  60 

1.  $156.  2.  $184.37. 

Page  62 

1.  $1300.75.  5.  $254.20.  9.  $92.56.  12.  $225.75. 

2.  $228.48.  6.  $125.28.  10.  $87.55.  13.  $443.88. 

3.  $219.30.  7.  $475.60.  11.  $110.70.  14.  $191.58. 

4.  $333.90.  8.  $223.48. 

1.  79,112.  2.  258,633.  3.  208,936.  4.  312,912. 

Page  63 

1.  a.  2484.   b.  2664.   c.  2682.   d.  8508.    e.  8514.  3.  $35,918,  gain. 

2.  a.  3312.   b.  3652.   c.  3576.   d.  11,344.   e.  11,352.      4.  $665.56. 

Page  64 

1.  1st  Balance,  total  $1409.95 ;  2.  1st  Balance,  total  $833.87  ; 

Checks,  total  $2369.11 ;  Checks,  total  $915.84  ; 

Deposits,  total  $1933.54  ;  Deposits,  total  $654.81 ; 

2d  Balance,  total  $974.38,  2d  Balance,  total  $572.84, 

check.  check. 

Page  65 

1.  $674.76.  3.  8206,  check.  6.  5456,  check.  7.  $35,918. 

2.  $1160.22.        4.  15,360,  check.  6.  33,225,  check. 

Page  69 
1.  $123.75.  2.  6500.  3.  950. 

Page  70 
4.  $4559.50.     6.  450  T.  8.  2000  bbl.        10.  $686. 

6.3106.  7.  $8290.65.     9.  100  shares.     11.  16- bu.;  $657,564,300. 

12.  Total  yield,  1,668,460,000  bu. ;  total  valuation,  $1,028,239,000. 

RE 


6  PRACTICAL  BUSINESS  ARITHMETIC 

Page  74 

1.  $10,010;  115,525.  3.  $11,446.70.  5.  37+  bu. ;  $443,939,481. 

2.  82g«gmo.  4.  $733.20. 

Page  75 

6.  (a)  1,601,754;  (6)  665.  7.  (a)  1,578,172;  (6)  641. 

8.  1910,  $3,654,243.54  ;  1911,  $3,742,305.63. 
9.  1910,  $2.22-  ;  1911,  $2.31-.     *  10.  $715,921,352.50. 

Page  76 

1.  108.  3.  80.  5.  294.  7.  615.  9.  395. 

2.  85.  4.  80.  6.  187.  8.  311. 

Page  81 

(The  small  figure  above  the  amount  indicates  the  price-list  number.) 

1.  $4749.80;  $4397.20;  $4862.60;  $5242.90;  $59n.45. 

2.  $4793.05;  $4392.45;  $5046.30;  $5416.10;  $6033.30. 

Page  82 

3.  $5419.35;  $4980.70;  $5522.65;  $5910.70;  $65^78. 

,  4.  $5177.55;  $4742.05;  $5196.35;  $5752.30;  $6310.16. 

Page  83 

6.  $6219.60;  $5776.35;  $6518.10;  $6760.50;  $7780.15. 
12  3  4  5 

6.  $7071.35;  $6510;  $7095.30;  $7614.90;  $8455.85. 

Page  84 

7.  $6232.80;  $5850.15;  $6304.15;  $6641.85;  $7332.25. 

12  3  4  5 

8.  $5798.30;  $5494.60;  $5847.20;  $6294.95;  $7233.80. 

Page  85 
1.  16  in.  2.  $2.35.  3.  $15,132. 

RE 


ANSWERS 


Page  86 

4.  16  yr.  5.  742  pupils.  6.  $0.70.  7.  63001b.;  631b. 

8.  Total  amount,  $153  ;  average  daily  wages,  $2.55. 


4.  24,877,125. 


Page  90 

6.  $738.71.  6.  $3099.60.  7.  $70,287.28. 


Page  93 

1.   .5;  .50;  .500.  2.  900.0011;  .0911;  500.002. 

3.  .000174;  174,000,000.000007;  7,000,000.000174. 

4.  7000.0075  ;  .0000257  ;  200.000046  ;  .000246. 

Page  94 

6    .4010097  ;  4,010,000.0000097  ;  .000500  ;  .00000005. 

6.  606.05001  ;  606.00051  ;  56.000000Q128. 

7.  17,000.001876;  17,000.1876;  21.16. 


Page  95 

9555.284126.        3.  96.3982201. 


4.  40,091.710245 


1.  255.6735. 

6.  2668.4189928. 

6.  Line  totals  :  $13,299.39  ;  $2897.30  ;  $5997.21  ;  $10,280.58  ;  $8359.91 
$17,856.91;  $16,173.09;  $21,845.56;  $8905.13;  $10,015.09;  $17,708.81 
$8521.80;  $23,641.05;  $13,323.26;  $11,306.09;  $14,185.56;  $9044.06 
$74,812.27;  $7399.48;  $16,290.70.  Column  totals:  $119,263.52;  $135, 
004.95;  $27,693.42;  $29,901.36.    Check,  $311,863.25. 


7.  5545.288766. 


4.3578. 

16.2155. 

.110745. 


Page  96 

1177.46.  7.  .000196. 

3.7325.  8.  7.50279. 

10.9999729.  9.  85.794. 


10.  254.012. 

11.  421.60071. 


12.  -03472^. 

13.  $2942.36,  gain, 


Page  97 

14.  $1697.93,  gain. 

15.  $2537.83,  gain. 


16.  $272.52,  loss ; 

$3176.91,  present  worth, 


Page  100 

1.  474.392.      3.  474.392.      5.  .189084.  7.  78,461.       9.  311.09078. 

2.  474.392.      4.  3217.1  6.  .00474392.      8.  3103.2.      10.  $159^375. 
11.  $4500.                     12.  355,333,000  bu. ;  $328,327,692,  total  valuation. 


8  PRACTICAL  BUSINESS  ARITHMETIC 

Page  102 

1.  127,000.       4.  .26.  7.  .4.  10.  146,600.  13.  .025. 

2.  24.  5.  720.  8.  .05.  11.  2500.  14.  .00000002. 

3.  .0002.  6.  5000.        9.  910,800.       12.  .00006.  16.  100,000,000. 

Page  103 

16.  18,090,999.100800909.  19.  444,044,016.444.  22.  .1 

17.  1,000,044.009.  20.  2.277525.  23!  fO.50. 

18.  5,550,511.1055.  21.  1,055,556.5001.  24.  200;  $40. 

Page  104 

26.  557,012,903  bu.;  $172,674,000,  total  valuation. 

Page  105 

1.  $2.48.  3.  $3.84.  6.  $11.36.  7.  $34.30. 

2.  $3.93.  4.  $1.85.  6.  $3.90.  8.  $27.28. 

Page  106 

1-  $70.  3.  $578.76.  5.  $8959.58.  7.  $227.17. 

2-  $6.08.  4.  $130.08.  6.  $233.68.  8.  $6648. 

Page  107  t 

1.  $14.64.  2.  $14.94.  3.  $3. 

Page  108 

1.  $13.28;  $12.91.  2.  $10.99;  $10.18. 

Page  109 

3.  $51.90.  6.  $423.68.  7.  $123.92.  9.  $1398.97. 

4.  $6.45.  6.  $157.35.  8.  $334.12. 

1.  653.3136.  2.  248.076.  3.  150  da.  4.  $6.72. 

Page  110 

6.  13,612.5.  9.  400  cd.  13.  A,  $2800  ;  B,  $3300  ; 

6-  $1305.  10.  $193.29.  C,  $2300. 

7-  $6.  11.  $50.50,  gain.  14.  $222.35. 

8-  $4.50.  12.  ^.  16.  $2346.05. 


ANSWERS  9 

Page  111 

16.  $173.66.  18.  $429.79.  20.  $2.06. 

17.  $4.781 .  19.  40  A.  21.  $56,299.99,  gain. 
22.  (a)  353.4975 ;    158.2824;    227.5579;    139.187;    111.2937;    164.901. 

(6)  381.217;  74.1416;  516.1397;  146.0072;  37.214.   Check,  1154.7195. 

Page  112 

1.  3010.2525.  4.  5060.61.  7.  3630.336. 

2.  24,388.8.  6.  333.693.  8.  3633.333. 

3.  30,045.6.  6.  1605.6.  9.  5556.0505. 

Page  114 

1.  2*,  7.  6.  32,  5,  7.  11.  2,  52,  13.            16.  22,  3,  52,  23. 

2.  2,  32,  7.  7.  28,  112.  12.  2,  3,  127.           17.  2*,  3,  43. 

3.  25,  32.  8.  13,  53.  13.  2,  3^,  151.          18.  28,  52,  37. 

4.  2,  3,  131.  9.  2,  32,  61.  14.  2^,  3*,  5. 
6.  28,  72.  10.  28,  3,  17.  15.  5,  641. 

Page  115 

1.  16.  2.  88.  3.  6.  4.  12,288. 

Page  116 

5.  $375.  7.  600  bu.  9.  $30.87. 

6.  80  da.  8.  180  men.  10.  1200  rm. 

Page  117 
1.  48.  2.  2.  3.  4.  4.  14. 


7.  600  bu. 

8.  180  men. 

Page  117 

2.  2. 

3.  4. 

Page  118 

5.  240. 

7. 

7875. 

6.  858,390. 

8. 

54,720. 

1.  840.  3.  288.  5.  240.  7.  7875.  9.  330. 

2.  504.  4.  2944. 

Page  122 

1.  \h  ^%  \h  T^.  \h  tV  3.  ^^^mi.;  £H;  f  lb. ;  ^,,  mi 

2.  ^%  cu.  ft. ;  j\  A. ;  ^  T.  4.  ^^  mi. ;  ^^ly  ^i-  5  ^% 
5.  IfT.;  I^T.;  fg-A.;  |^A.;  ^^sq.mi.;  |f  g  sq.  mi. ;  f  1  mi 


mi, 


BE 


10  PRACTICAL  BUSINESS  ARITHMETIC 


Page 

123 

' 

1. 

^F- 

4. 

2.D0fl._ 

7.  l^//i. 

10.    i8|AA. 

2. 

-|^- 

5. 

Hi''- 

8.  A|oiL. 

11.    5J7_^5X. 

3. 

J^O. 

6. 

-LV^^- 

9-  ^11-- 

12.    2^/^. 

1.  2|^mi. 

4.  lOf  A. 

7. 

1531 

lb. 

2.  12tVA. 

6.  41  IT.     • 

8. 

51  cu 

.ft. 

3.  4i|| 

r. 

6.  3^A'oT. 

9. 

14 1  sq.  mi. 

Page 

124 

1. 

II,  if,  U- 

6.ff8 

^HlHhjVo-   11- 

bV^,  II  &, 

^Vo,  \%% 

2. 

f  §,  l§,  A- 

7.  if, 

f  i  II, 

l|.              12. 

rh, 

II,  ^\,  l|. 

3. 

^1,  f -1,  t\, 

T«l^ 

. 

8-  IIS 

,A%,tVo,t¥o-     13. 

31f  1,  7^0 

4. 

M,  i%.  %h 

n 

. 

9-    7^4 

,t\\,t\VtI4-     14. 

134^io,  1123^00. 

5. 

It,  II,  M, 

u 

• 

lO-  II, 

II,  II, 

II-              15. 

6126 

II,178H. 

Page 

126 

1. 

'tV.           4. 

31] 

i- 

7. 

185/^. 

10.  242 1 

13.  $374.40 

2. 

If.           5. 

24^^o- 

8. 

37|. 

11.  2181|§. 

14.  $583.38 

3. 

19|.          6. 

32H- 

9. 

221i|. 

12.  1153 

iV 

Page 

129 

1. 

29,332/(.. 

4. 

38,3171. 

7.  102,857| 

10. 

90,288^9_ 

2. 

19,657. 

5. 

37,807 

8.  99,313f . 

11. 

58,893^1 

3. 

21,337/^. 

6. 

49,097 

Page 

9.  97,868f . 
131 

12. 

42,3601. 

1. 

271. 

4. 

138ii. 

7.  160||. 

10. 

t\' 

2. 

631. 

5. 

124M- 

8.  2028  iV- 

11. 

2M- 

3. 

122^. 

6. 

228VV. 

Page 

9.   2V- 
133 

12. 

U- 

1. 

61i. 

7. 

83J. 

13.  560. 

19. 

2016|. 

2. 

53^. 

8. 

17f. 

14.  51. 

20. 

2187^. 

3. 

14tV. 

9. 

70*. 

15.  25. 

21. 

2160. 

4. 

67A- 

10. 

28}i. 

16.  357. 

22. 

31981. 

5. 

28|. 

11. 

20f. 

17.  15lf. 

23. 

3173f. 

6. 

2it. 

12. 

33|>. 

18.  750. 

24. 

448. 

1. 

P70.51. 

2.  1215.97 

Bl 


ANSWERS  11 

Page  134 

3.  !|55.68.  4.  $97.34. 

Page  135 

\.  ^^^.  3.1121.  6.266.  7.  $169.  9.  $62.50; 

2.  If.  4.  326|.  6.  66.  8.  |2.72,  gain.  $218.75. 

Page  136 

10.  $62.50;  $203.13. 

11.  23.22  gr.  pure  gold,  2.58  gr.  alloy;  116.1  gr.  pure  gold,  12.9  gr.  alloy. 

12.  19.29  gr.  nickel,  57.87  gr.  copper.         13.  412.8  gr.;  371.^2  gr. 

1.  18,042|.  3.  15,679^V-  ^'  8455^2. 

2.  19,178-11.  4.  20,827^.  6.  934911. 

Page  137 
1.  $5268.75. 

Page  138 
1.  $503.50.  2.  $2602.50. 

Page  141 

1.  \^%.       4.  1171.       7.  1^.           10.  4|.            13.  1^\.  16.  119^\. 

2.  60.           6.  26|.         8.  7-,L.         11.  35|.           14.  2^^-  ^'^'  H- 

3.  152.        6.  77^.         9.  l^,.        12.  68t\.        15.  34§.  18.  12||f. 

1.  211§.          3.  69-i§|.          5.  24tV^.          7.  96.  9.  6t^\V 

2.  16|il.        4.  30|.  6.  36|t|.  8.  27^-^7. 

Page  143 

1.  Cost,  $100 ;  asking  price,  $140 ;  4.  First  cost,  $32;  marked  price, $48. 
selling  price,  $126.  5.  $6300. 

2.  Bonds,  $1440 ;  bank  stock,  $900.  6.  Oats,  3300  bu. ;  wheat,  1100  bu.; 

3.  $18,672.  rye,  1650  bu.;  $3313.75. 

Page  144 

1.  9,000,000  ;  7,200,000.  3.  76,800,000  ;  12,800,000. 

2.  3,136,000  ;  224,000.  4.  | ;  ^  ;  31,443,324. 

5.  1,907,210. 
RE 


12  PRACTICAL  BUSINESS  ARETHMETIC 

Page  145 

1-  I-  «•  U-  9-  ^Uu-  13.  260f^. 

2.  tV-  6.  1§.  10.  T^^^.  14.  126^^. 

3-  ^hs-  7.  ^7^.  11.  181^.  16.  175^^. 

4-  i'^-  8.  i-  12.  171^^.  16.  1725a_. 

1.  .875.  4.  .4375.  7.  .035416.  10.  5.5833+. 

2.  .3125.  6.  .028125.  8.  .28.  11.  21.625. 

3.  .5625.  6.  .6875.  9.  .00078125.         12.  165.85. 

Page  148 

2.  $29.82.  4.  219f  da.  6.  250  bu.;  585  bu. ;  1295  bu. 

3.  51  men.  6.  10  wk. 

Page  149 
1.  121.77.      2.  $154.22.      3.  $1.70.      4.  $6.25.      6.  S^^f.      6.  3/2  da. 

Page  150 

7.  $105.         9.  $4.31.  11.  262  da.  13.  $8599.22.       16.  $8.50. 

8.  $3.59.      10.  $222.75.        12.  $97.50.  14.  $259.15.        16.  $1542.63. 

17.  $1.52  ;  $2032.65.  18.  A,  $50;  B,  $77.50  ;  C,  $132  ;  D,  $160. 

Page  151 

19.  $566.29,  gain.       20.  $51.81,  gain.       21.  $179.31.       22.  $43.87,  gain. 

23.  ^  ;  50%  ;   60f  ;   A,  $356.13  ;   B,  $710.63  ;   C,  $312.62  ;   D,  $730.37. 

24.  $621.63. 

Page  152 
26.  $1136.23.        26.  $36.09.        27.  $14.44.        28.  $4.69.         29.  $31.50. 

Page  156 

1.  $1.64-.  3.  If;  ^1.  6.  $2.25.         .  7.   |  ;  $5.  9.  $22.20. 

2.  $1.68.  4.  II;  ^\.  6.  $2.80.  8.  $33.60. 

Page  157 

1.  A,  $21.60;  B,  $32.40;  C,  $27.  3.  $48.  5.  ^. 

2.  $21,756.69;  $25,382.81.  4.  $150.  6.  $56;  f 

7.  6|;  4^\;  7^  ;  2^ ;  14| ;  3^;  2^V  5  H '^  ^^'2  5  3^1 ;  4-,^ 

8.  f  ;  $135. 

9.  A,  1  $1530.45;  B,  ^,  $1020.30;  C,  ^,  $510.15. 


ANSWERS 


13 


Page  160 
1.  $210.  2.  $292.75. 

Page  163 
1.  14897.90.  2.  1410.92.  3.  |5705.11. 


3.  $680.25. 


1.  $19,631.33. 

2.  $54,934.83 ;  $2856.25. 


Page  165 

3.  $204.69. 

4.  $537.59. 

Page  166 

6.  b.  $426.74. 


4.  $2125.76. 


6.  $2487.46. 
6.  a.  $198.69. 


1.  760  yd. 

2.  816  yd. 


3.  3660  yd. 

4.  2252  yd. 


Page  167 

5.  6916  yd. 

6.  5163  bu. 


7.  7370  bu. 

8.  2040  bu. 


9.  6426  bu. 
10.  16,323  bu. 


Page  169 

(The  small  figures  indicate  the  price-list  number.) 

12  3  4 

$59.72;  $62.33;  $57.84; 
$201.30;  $211.72 
$95.74 ;  $100.92 
$212.20  ;  $204.05 


$56.63 ; 

$191.36 

$87.97  ; 

$197.64 
6.  $145.91 
6.  $201.54 


$195; 
$97.06 ; 
$201.52 

$155.42 
$198.14 


1.  $103.75. 


$163.09;  $166.58 
$204.09;  $202.67 

Page  176 
2.  $441.84. 


5 

$64.97 ; 
$215.96 
$108.06 

$218.74 
$173.06 

$214.41 


$67.14. 

$229.22. 
$112.03. 

$227.20. 
$183.24. 
$224.89. 


3.  $333.75. 


Page  177 

4.  $51.87.    5.  $450.30.    6.  $922.32.    7.  $882.33.    8.  $155.77.    9.  $547.12. 


Page  178 

10.  $1353.45.  12.  $260.56.  14.  $52.81. 

11.  $4329.50.  13.  $305.92.  15.  $56.3?. 


RB 


1.  $573.50. 


Page  180 
2.  $1254.20. 


16.  $515.68. 

17.  $203.25. 


3.  $65. 


1 


14  PRACTICAL  BUSINESS  ARITHMETIC 

Page  182 

1.  $149.81 :  11  pennies,  3  nickels,  8  dimes,  7  quarters,  8  halves,  4  I's, 
12  2's,  7  6's,  and  8  lO's. 

Page  183 

2.  $227.20.  3.  20  pennies,  4  nickels,  8  dimes,  6  quarters,  7  halves, 

4  I's,  16  2's,  7  5's,  9  lO's,  and  3  20's. 
1.  $2690.76. 

Page  184 

2.  $804.71.  3.  $5631.88. 

Page  185 

4.  $155.95  :    15  pennies,  5  nickels,  3  dimes,  5  quarters,  4  halves,  7  I's, 

5  5's,  6  lO's,  and  3  20's. 

Page  187 

1.  $3.12.  2.  $3.87.  3.  $88.65. 

Page  188 

4.  $30.25.  6.  $19.56  ;  $13.61 ;  $25.31 ;  $21.48. 

5.  $35.87;  $29.87.     7.  $52.58;  $53.49;  $75.68;  $95.84;  $115.72;  $125.37. 

Page  192 

1.  1386  in.  3.  335s.  5.  57.75  ft.  7.  522,720  sq.  ft. 

2.  48-1  pk.  4.  41,814  in.  6.  48,000  oz.  8.  20,608  cu.  ft. 

1.  3520  ft.  3.  32,397f  sq.  ft.  6.  1980  ft. 

2.  96cu.ft.  4.  31iin.  6.  300  sec. 

Page  193 

1.  232  rd.  4  yd.  7.  33  sq.  yd.  5  sq.  ft.  72  sq.  in. 

2.  131gal.  3qt.,orl6bu.  Ipk.  7qt.  8.  13  T.  19  cwt. 

3.  4  hr.  9.  76  rd.  2  yd. 

4.  1  sq.  yd.  4  sq.  f  1. 128  sq.  in.  10.  400  cd. 

6.  204  bu.  11.  3  cu.  yd.  3  cu.  ft. 
6.  20  mi.  60  rd.       *  12.  17431b.  12  oz. 

1.  /^ft.;   /^yd.  2.  £5375.  3.  .818  rd.  4.  £527. 

5.  5.3605  T.;  6.875  T.;  12.145  T.;  14.62  T.;  14.195  T. 

6.  $5.47;  $6.78;  $2.16;  $4.25;  $10.13;  $101.84. 


ANSWERS  15 

Page  195 

1.  £1180  88.  6.  2  mo.  16  da.  9.  30f  cd. 

2.  £2134  9s.  6.  1  mo.  10.  $20,512.50. 

3.  582  T.  489  lb.  7.  6  mo.  15  da.  11.  £1198  14s.,  gain ; 

4.  3087  T.  990  lb.  8.  6  mo.  16  da.  $5833.47,  gain. 

Page  196 

1.  237  da.  3.  232  da.  6.  254  da.  7.  94  da. 

2.  201  da.  4.  254  da.  6.  133  da.  8.  163  da. 
9.  2 yr.  7 mo.  18 da.;  lyr.3mo.27da.;  5 yr. 8 mo. 25 da.;  17yr.9mo.21da. 

Page  198 

1.  $12.86;  $13.38.  3.  500  mi.  6.  $43,666.25. 

2.  $67,671.87.  4.  $2,  gain. 

Page  199 

7.  £93  Is.  6d.;  $452,95.      9.  $28.83;  $17.52.      10.  £45  19s.  3d.;  $223.68. 

Page  200 
11.  $23.96.  1.  $268.09.  2.  $216.41.  3.  $642.49. 

Page  202 

2.  $17.22. 

Page  203 

3.  36  ft.;  131.9472.  4.  $7.92.  6.  4800  poles. 

Page  205 

1.  1114.308  sq.  yd.     2.  54.45  ft. ;  $5445.     3.  4500  tiles.     4.  8946  sq.  ft. 

Page  206 
3.  $288,000.  4.  $2000. 

Page  208 

1.  18.  5.  24.  9.  95.  13.  ^. 

2.  22.  6.  32.  10.  58.  14.  {|. 

3.  26.  7.  85.  11.  8.4.  16.  ||. 

4.  27.  8.  63.  12.  12.26.  16.  |f  |. 

RE 


16  PRACTICAL  BUSINESS  ARITHMETIC 

Page  209 

1.  30  rd.  2.  120  rd.  -    3.  50  ft.  4.  |190.  6.  $28. 

Page  211 

2.  33,750  shingles. 

Page  212 

3.  17,500  shingles.  1.  |205.20.  2.  f21.71. 

Page  213 

3.  $101.70. 
1.  |24.  2.  $7.61.  3.  $122.67  4.  $146.67 ;  $149.11. 

Page  214 

1.  $19.22.        3.  1231  sq.  ft.  hard  wood  ;  1154  sq.  ft.  spruce.     6.  $42.90. 

2.  $118.13.      4.  $79.26.  6.  $312.94. 

Page  216 
1.  20  yd.  2.  181yd.  3.  $22.92.  4.  30  yd.  5.  23^  yd. 

Page  218 
1.  $7.60.  2.  8  rolls.  3.  $3.44. 

Page  219 

1.  140/^cu.  yd.  2.  135  on.  ft.  3.  $8050. 

Page  220 

1.  llicd.  2.  40  ft.  3.  600  ft.  '         4.  4  ft. 

Page  223 

1.  21331ft.  3.  2560  ft.  5.  1600  ft.  7.  $36.78. 

2.  390  ft.  4.  3733^  ft.  6.  3600  ft.  8.  $332.05. 

Page  224 

1.  $26.76.  2.  $39.79.  3.  $29.45. 

1.  3240  gal.;  3231.58  gal.  3.  900  gal.;  897.66  gal. 

2.  2120.58  gal.;  2115.07  gal.  4.  26,507.25  gal. ;  26,438.4  gal. 


ANSWERS  17 

Page  225 

1.  132.12,  or  about  133  perches.        2.  67.88,  or  about  68  perches. 
3.  (a)  109.63,  or  about  110  cu.  yd. 
(6)  102.22,  or  about  102  cu.  yd. 

Page  226 

1.  45,738  bricks.     2.  |712.80.     3.  (a)  203,500  bricks ;  (&)  198,550  bricks. 

Page  227 

1.  460.8  bu.  3.  4  ft.  5.\  in.  5.  42.18  bu.  7.  33.08  bu. 

2.  42  bu.  4.  462.8  bu.  6.  362.88  bu. 

Page  230 

(Problem  1  includes  problems  1-12  on  pages  189,  190.) 

1.  $507.31.  4.  $426.13.  7.  |545.96.  10.  $515.06. 

2.  $700.15.  6.  $414.98.  8.  $430.51.  11.  $637.58. 

3.  $641.86.  6.  $1107.98.  9.  $694.76.  12.  $339.99. 

Page  234 

1.  $656.  3.  $3.  5.  $4050. 

2.  A,  $453.60  ;  B,  $750  ;  C,  $2250.  4.  $2847,  gain.  6.  $2503.91. 

Page  235 

1.  16%.    2.  80%.    3.  4%.    4.  21%.    6.  Smith,  58% ;  Brown,  42%.    6.  11%. 

Page  236 

1.  $4000.^     2.  $60,803.       3.  $20,625.       4.  $359,100.  '    6.  2275  students. 

Page  237 
1.  $0.95.  2.  $6.  3.  $147.63. 

Page  238 

1.12,444.  2.  $0.64.  3.  $125.  4.  212  papers.  5.  43bbl. 

Page  239 
1.  $155.02.      2.  $23,477.20;  $14,086.32.      3.  3^%;  3200%.     4.  $2494.17. 

Page  240 

6.33^%.  T.  4^%.       9.  $1491.      11.  1900% ;  96%. 

6.  54%  ;  46%.       8.  $4000.      10.  88.8%. 

BE 


18  PRACTICAL  BUSINESS  ARITHMETIC 


Page  241 

12.  $2400. 

14.  A,  175,000;  B,  150,000;  C,  125,000 

13.  764%. 

A,  38|%;  B,  331%;  C,  27^%. 

15.  United  States, 

450,000,000  T.  ;  48.6% 

Great  Britain, 

250,000,000  T.  ;  27% 

Germany, 

175,000,000  T.;  19% 

France, 

50,000,000  T.;  5.4% 

Other  countries. 

200,000,000  T.  ; 

1,125,000,000  T. 

Page  242 

16.  25.2%.  17.  22|% 

18.  Corn,  24.1%  decrease  ;  wheat,  3.1%  increase  ;  oats,  20.8%  decrease  ; 

barley,  21.5%  decrease  ;  rye,  2.8%  decrease  ;  buckwheat,  26.3%  decrease. 

Page  243 

20.  Total,  27,323,055  ;  men,  22,489,425  ;  women,  4,833,630 ; 


Per  Cent 

Total 

Men 

Women 

N.  Atlantic 

30.3 

29.1 

35.9 

S.  Atlantic 

13.1 

12.3 

16. 

N.  Central 

33.7 

35.1 

27.2 

S.  Central 

16.8 

16.9 

16.9 

Western 
Totals, 

6.1 

100% 

6.6 
100% 

4. 

100% 

Jl. 

26.3%  ;  20.8%  ;  79.2%  ; 

380%. 
Page  245 

1.  16,000%. 

2.  $2250. 

3.  14.8%. 

4.  $606.14;  $11.71. 
6.  $196.52. 

6.  1st  mo.  $2400 
3d  mo.  $3600 ; 

7.  121.3%. 

8.  $1800. 

Page  248 

;  2d  mo.  $3000  ; 

4th  mo.  $3240. 

1. 

2. 

$2268.           3.  $3000. 
$1872.           4.  $1710. 

5.  2916. 

6.  $1760. 

7.  100  yd.           9.  $244. 

8.  $135.72. 

Page  249 

10.  The  second;  $1.     11.  $432,  gain.     12.  a.  $307.67.  6.  $51.  c.  $888.25. 

Page  250 

1.  73%.  3.  $550.  5.  $540. 

2.  A  single  discount  of  65%  ;  13%.  4.  5^%.  6.  $1687.50. 

^,.  RE 

'lO 


ANSWERS  19 

Page  252 

1.  |288.  2.  156.25.  3.  !|675.90.  4.  |1200.  6.  |1083.46. 

Page  253 
1.  184.38  2.  $720,  gain.  3.  fl323.  4.  |3199.39. 

Page  254 

6.  $3020.87;  f3083.16  ;  $3103.41;  $3167.40.  7.  $41.61. 

6.  £340  63.  3d.;  $1656.13.  8.  $400.55. 

Page  255 

1.  331%.  3.  22f%.  5.  33JL%.  7.  $270.  9.  $107.53. 

2.  25%.  4.  28f%.  6.  $800.  8.  $341.89. 

Page  257 

1.  $49.27.  3.  $2.50,  loss.  6.  $136.50 ;  $796.50. 

2.  $3470.83.  4.  $190  ;  $3990. 

Page  258 

1.  140%.  3.  100%.  6.  $300,  gain ;  33^%.- 

2.  140%.  4.  $230,  gain ;  33^%.  6.  25%. 

Page  259 

1.  $72.  2.  $85.    .  3.  $18.60. 

Page  260 

4.  $1600,  loss.  5.  $6451.50.  6.  $14.  7.  $120. 

1.  20%.  2.  12i%,  gain.  3.  $3800.  4.  $8467.20. 

/     Page  261 
6.  $17,404.80.    .  7.  $990.  9.  $16.  11.  $216 ;  32%. 

6.  $6072 ;  30.67%.  8.  $162,  gain.         10.  $675.  12.  $5.73. 

Page  263 

2.  $16,300.         8.  26%.         4.  $81.43.        5.  $1620.        6.  6^% ;  $110.03. 

Page  265 

J    eAb^^        ^   hAJ^  ^^  pAa  ^^   y^  ^^    rj-.ii  + 

'r.wy  '  t.  r  e  r.ao  ux  in.mE 


r.  8  n 


rl.un         ^    eu.ns         ,,1'-  ,.    ri.  h  + 


r^j_n  l_^iii_^.       8.^-^^^^-^.       11.-^.  14. 


p.  r  e  'ew.hd  'ep.ay  -L  ^  T3-u# 

!i^  9   i-tl^.       12.  ^. 

to.  Tl.  3#,  1^ 


Z.AHL  6.^.  9.  i-tl^.      12    '"-' 


.a  m 

RE 


20  PRACTICAL  BUSINESS  ARITHMETIC 

Page  267 

1.  $625.  2.  !|40.  3.  fO.50.  4.  f4.80.  6.  fO.60. 

Page  268 
6.  Bookcases,  $14.40  ;  chiffoniers,  |21. 60. 

^-  ^^^^TTT'    pencils,—-—;    cards,  ^. 
0.  ht  f.ht  .fa 

Page  269 

2.  $2.35.  3.  12^%.  4.  $0.41. 

Page  273 

2.  $2842.  4.  $3880.82,  proceeds.  6.  $430.50. 

3.  $1293.60.  5.  $1142.32.  7.  $235.20. 

Page  274 

8.  $225.     9.  $366.69,  proceeds ;  $6.69,  gain.     10.  $1649.80,  net  proceeds. 
1.  $3.75;  $2730.    2.  $200;  $81,450.    3.  $1037.50.    4.  $262.50.    6.  $6971. 

Page  275 

6.  $7563.75.       7.  $243.75 ;  $173,243.75.       8.  $834.75.       9.  2%  ;  $5319. 


Fack  of 
Debt 

1.  $457.75 

2.  $259.00 

3.  $175.50 

4.  $325.45 
6.  $182.40 

6.  $255.50 

7.  $112.75 

8.  $282.00 

9.  $258.00 

10.  $424.00 

11.  $455.95 

12.  $132.00 

13.  $2375. 


Page  276 

Rate  of 

Agent 

Principal 

Commission 

Received 

Received 

2% 

$9.16 

$448.59 

1% 

$2.59 

$256.41 

3% 

$6.27 

$170.23 

2% 

$6.51 

$318.94 

5% 

$9.12 

$173.28 

4% 

$10.22 

$245.28 

4% 

$4.51 

$108.24 

H% 

$4.23 

$277.77 

mo 

$6.45 

$251.55 

Hlo 

$14.84 

$409.16 

2% 

$9.12 

$446.83 

5% 

$6.60 

$125.40 

14.  4%. 

15.  $357.50. 

ANSWERS  21 

Page  282 

1.  $210.  2.  $31.25;  $78.13.  3.  $32.  4.  $168 ;  $4218.75. 

Page  283 

6.  A,  $3000  ;  B,  $2500  ;  $90 ;  $75.  7.  $252. 

6.  $8071.65.  8.  $5600;  $1600. 

9.  $55.33  ;  A,  $2000  ;  B,  $2400  ;  C,  $1600. 
10.  ^tna,  $10,366.67 ;  Continental,  $3887.50  ;  Ger.  Am.,  $5183.33. 

Page  284 

11.  $50.90,  less.  12.  In  full :  B,  $1500 ;  D,  $7000. 

Page  285 

1.  A,  $5400  ;  B,  $5100.  3.  $556.25  ;  $2443.75. 

2.  $2540;  $38.10.  4.  $25,856.60;  $387.86. 

6.  $180  ;  $138.88  ;  $9258.88. 


Page 

288 

1.  $63.60. 

4.  $65. 

7. 

$780,000. 

2.  $44.73. 

6.  $82.40. 

8. 

$575,000. 

3.  $52.06 

6.  $240,000 
Page 

1. 
289 

9. 

$0.012 ;  $94.90. 

10.  $16.50. 

12.  B,  $479.50 ;  C 

;,  $876. 

14. 

$9;  $19. 

11.  $0,017. 

13.  $0,006. 

Page 

290 

1.  $46.22. 

9.  $641.70. 

17.  $103.32. 

25.  $356.93. 

2.  $22.32. 

10.  $1534.50. 

18.  $140.90. 

26.  $488.44. 

3.  $19.53. 

11.  $1827.45. 

19.  $54.48. 

27.  $1596.81. 

4.  $86.12. 

12.  $406.41. 

20.  $88.29. 

28.  $1465.31. 

5.  $157.69. 

13.  $372. 

21.  $178.47. 

29.  $394.51. 

6.  $245.52. 

14.  $517.08. 

22.  $163.44. 

30.  $1671.95. 

7.  $273.42. 

15.  $1333.43. 

23.  $122.11. 

31.  $187.86. 

8.  $342.24. 

16.  $1670.28. 

Page 

24.  $136.20. 
295 

32.  $394.61. 

1.  $3062.60. 

2.  $365.80. 

3.  $6568. 

90. 

4.  34;*-. 

RE 

22 


PRACTICAL  BUSINESS  ARITHMETIC 


1.  $24.50. 

2.  $170.45. 

3.  $170.45. 

4.  $434.35. 
6.  $1200. 


Page 

6.  $404. 

7.  $9.50. 

8.  $537.60. 

9.  $28,486.80. 


296 

10.  $542.70. 

11.  $200. 

12.  $965. 

13.  $2142. 


14.  $119. 
16.  $1509.90. 

16.  $2380. 

17.  $3319.75. 


1.  $2.70+. 


Page  297 


2.  $365.36. 


3.  £136  16s.  lOd. 


Page  298 

4.  $657.46;  $229.95. 


6.  72^- 


6.  8%+  ; 


1.  $5.58.       4.  $4.20. 

2.  $2.45.       5.  $7.20. 

3.  $4.52.       6.  $5.52. 


Page  299 

7.  a.  $40.80.     6.  $96.15. 

Page  302 

7.  $4.35.       10.  $10.07. 

8.  $13.41.     11.  $1.19. 

9.  $11.20.     12.  $3.65. 


13.  $4.70.       16.  $2.68. 

14.  $5.45.       17.  $6.90. 
16.  $1.26.       18.  $4.44. 


1.  $88.13 

2.  $21.53 
3. -$17.11 
4.  $65.10 


Page  303 

$34.27;  $39.17;  $29.38. 

$6.73;  $14.80;  $9.42;  $10.77. 

$4.89;  $9.78;  $12.22;  $2.44;  $24.44. 

$86.81;  $13.02;  $39.06;  $78.12;  $69.44;  $60.76;  $26.04. 

Page  304 
1.  $399.35. 


2.  $338. 
1.  $11.20. 


Page  305 

3.  $195.42. 

Page  306 
2.  $19.53. 


4.  $449.96. 


3.  $41.62. 


1.  $120. 

2.  $318. 

3.  $304. 


Page  307 

4.  $79.  7.  $560.03. 

6.  $742.05.  8.  $1875.20. 

6.  $336.09.  9.  $41. 


10.  $0.21. 

11.  $29.82. 

12.  $28.27. 

BE 


ANSWERS 


23 


1.  $6.30. 

2.  $10.83. 

3.  $3.68. 

4.  $0.63. 
6.  $1.77. 


1.  $80.25. 


6. 
7. 
8. 
9. 
10. 


$8.25. 

$2.15. 

$3.22. 

$4. 

$0.08. 


Page  308 
2.  $250.53. 

Page  309 

11.  $6.75. 

12.  $5. 

13.  $14.40. 

14.  $2.10. 
16.  $4.20. 


3.  $113.71. 


16.  $7.35. 

17.  $1.48. 

18.  $0.84. 

19.  $0.73. 

20.  $2.52. 


1.  $1.62. 

2.  $44.12. 

1.  $5.8Y. 

2.  $8. 


3.  $103.87. 

4.  $23.29. 


Page  313 

5.  $191.59. 

6.  $95.08. 

Page  314 


7.  $48.26. 

8.  $98.23. 


3.  $262.50. 

4.  $467.50. 


5.  $2.84. 

6.  $4.83. 


9.  $266.22. 
10.  $142.83. 


7.  $82.87. 

8.  $159.50. 


Page  316 

4.  $1301.04;  $735.17;  $1836.13. 


1.  $14.97. 

2.  $5.13. 

3.  $7.59. 

4.  $9.22. 


5.  $5.37. 

6.  $2.56. 

7.  $10.20. 

8.  $11.97. 


Page  317 
9.  $690.41. 

10.  $1849.32. 

11.  $92.81. 

12.  $129.45. 


13.  $37.97 

14.  $66.24 
16.  $10.76 


$56.96. 

$22.08. 
$16.14. 


16.  $130.41;  $86.94. 


J  Page  319 

1.  Time  offer .'^-';  3.  Cash  offer.  ^^  -  6.  $1777.78. 

2.  Time  offer./,  ^         4.  $5.60,  gain.  6.  $77.16. 


7.  $1200. 


1.  $394.40.         2.  $144.21. 


Page  320 
3.  $43.20.        4.  $1943.73. 


6.  $1892.40. 


1.  $802.94. 


1.  $1624.88. 

2.  $670.60. 


Page  321 

2.  $156.12. 

Page  322 

3.  $5542.82. 

4.  $2139.38. 


3.  $811.82. 


6.  $1876.94. 
6.  $3732.25. 


24  PRACTICAL  BUSINESS  ARITHMETIC 

Page  324 

1.  $624,317.55.  2.  $38,937.24.  3.  $6996.81.  4.  $1000. 

1.  $11.94.  2.  $76.  3.  $1065.60.  4.  $994.70. 

Page  325 

6.  $248.27.  6.  15%.  7.  36%.  8.  $8.75.  9.  $19,978. 

Page  329^ 

1.  Apriri6;  46  da.  4.  April  ^  ;  21  da.  7.  April  11 ;  27  da. 

2.  Feb.  261  a^a.  6.  June  29  ;  47  da.  8.  July  30  ;  57  da. 

3.  May  1^  ;  7i  da.  6.  April  8  ;  58  da.  9.  June  18  ;  89  da. 

•?        ' 

Page  331 

1.  $4.90;  $1045.55.  3.  $1.95;  $298.05. 

2.  $1.84;  $243.69.  4.  $2.07;  $458.73. 

Page  332 
6.  $3.19;  $793.21.  7.  $1004.85.  9.  $669.60. 

6.  $877.24.  8.  $1249.18.  10.  $670.66. 

Page  333 

11.  No.  20,  July  25  ;  38  da. ;  $12.67  ;  $1987.33. 
No.  21,  Aug.  1 ;  45  da.  ;  $26.25  ;  $3470.25. 
No.  22,  June  30  ;  13  da.  ;  $3.25  ;  $1496.75. 
No.  23,  July  14  •  27  da. ;  $4.05  ;  $896.55. 
No.  24,  July  15  ;  28  da.  ;  $1.77  ;  $376.75. 


12.  $427 

3.39. 

13. 

$254.59. 

Page  334 

14.  $973.74. 

Page  335 

1.  $4925. 

2.  $1188. 
Page  336 

3. 

$12,032.50. 

4.  $15,083.13. 

1.  $2000 ; 

$2010.10. 

2.  $4000. 

Page  337 

1. 

2. 
3. 

Face 
(Totals) 

$2100.85 

$1584.84 

$2227.82 

Discount                Coll.  &  Exch. 
(Totals)                      (Totals) 

$17.55                        $1.87 

$13.54                       $1.59 

$19.05                      $1.85 

Proceeds 
$2081.43 
$1569.71 
$2206.92 

ANSWEKS  25 

Page  340 

1.  $525.  3.  $419.85. 

2.  $1979.17;  $1038.55;  $562.89.     4.  a,  $235.31;  6,  $472.11;  c.  $3802.33. 

Page  344 

1.  $233.85  ;  $1.46  more  by  the  United  States  rule.  3.  $5086.87. 

2.  $515.36.  4.  $313.13. 

Page  345 

6.  $317.91;  $4.79  more  by  the  United  States  rule.  6.  $6054.45.  7.  $219.94. 

Page  348 
1.  $2112.22.  2.  $5.78;  $4050.53.  3.  $1816.48. 

Page  351 

1.  $308.85;  $932.61.  2.  $813.50,  balance,  July  1,  1915. 

3.  $783.57,  balance,  Jan.  1,  1916. 

Page  353 

1.  $84.28  ;  $85.12.  3.  $73.44.  6.  $50 ;  $50.22. 

2.  $72 ;  $72.48.  4.  $97.52. 

Page  357 
1.  $75.30.  2.  $134.49.  3.  $1292.95. 

Page  362 

1.  $3962.71 ;  $680.14  ;  $768.92.  2.  $250  ;  $1  per  $1000. 

Page  363 

3.  $850.  5.  $712.65. 

4.  $1.70,  collection;  $2906.70,  proceeds.     6.  No  answer  can  be  given  here.  > 

Page  365  ^ 

1.  $497.83.  2.  $3484.25.  3.  $1149.13. 

Page  366 
4.  $6321.66. 

Page  368 

1.  3^1^%  discount ;  $17,113.42;  $12,923.29;  $127,099.31. 

2.  $178.05;  $477.80 


26  PRACTICAL  BUSINESS  ARITHMETIC 

Page  369 

3.  $16,841.45.         5.  $373.94. 

4.  $6789.69.  6.  $43.38,  total  charges  ;  $42,907.87,  total  proceeds. 

Page  370 

1.  £25.3;  £150.75;  £200.525;  £300.6375.  2.  $124.10;  $586.17. 

3.  $65.45;  $357.18;  $60.80;  $139.93;  $562.20;  £256  17s.  2d. 
6476.68  fr.;  5252.1  M. 

4.  $20,992,790. 

Page  373 

1.  $14,062.50.        3.  54steres;  14  ^^^  cd.        5.  $284,  gain.         7.  $2.27. 

2.  $114.24.  4.  $1.38.  6.  .97  mi.  8.  2  hr. 

Page  374 

1.  246.91  guilders.  2.  £10  5s.  4d.  3.  $50.  4.  $25. 

Page  377 

1.  a,  $487.50  ;  6,  $5850  ;  c,  $8775  ;  d,  $64.60  ;  e,  $96.90  ;  /,  $484.50  ; 
g,  $47.69  ;  h,  $38.15  ;  i,  $476.88  ;  j,  $1430.63  ;  k,  $953.75  ;  I,  $2861.25. 

2.  a,  $485.50  ;  6,  $5826  ;  c,  $8739  ;  d,  $64  ;  e,  $96  ;  /,  $480  ;  g,  $47.44  ; 
A,  $37.95  ;  i,  $474.38  ;  j,  $1423.13  ;  k,  $948.75  ;  Z,  $2846.25. 

1.  $2661.93.  2.  $24,275.  3.  £4900. 

Page  378 
4.  $867.38.  5.  $20,190.  6.  $198.  7.  £4825.  8.  £120. 

Page  379 
9.  $322.86.  10.  $23,359.03.  11.  $23,365.06.  12.  £4776  15s. 

Page  380 
13.  $2064.19. 

Page  382 
1.  $244.93. 

Page  383 
2.  $4902.21. 
1.  £1078  8s.  9d.  2.  $3524.46.  3.  $7127.27.  4.  $5054.42. 

RE 


ANSWERS  27 

Page  387 

1.  March  13,  1916.  4.  June  18,  1916.  7.  Nov.  3,  1916. 

2.  April  16,  1916.  5.  May  16,  1916.  8.  Dec.  29,  1916. 

3.  Sept.  18,  1916.  6.  Feb.  28,  1917.  9.  Dec.  11,  1916. 

10.  July  12,  1916. 
Page  391 

1.  Jan.  4,  1916.  3.  April  12,  1916.  6.  April  6,  1916. 

2.  Dec.  24,  1915.  4.  May  10,  1916. 

Page  392 
1.  July  11.  2.  July  31. 

Page  394 
1.  $201.86.  2.  $2082.34. 

Page  395 

3.  $1089.26.  4.  $1302.02.  5.  $741.47.  6.  $1054.31. 

Page  400 

1.  $2000.  3.  $2200.  6.  $50,000 ;  $2375.  7.  $48,750 ;  $1300. 

2.  $3375.  4.  4|%.  6.  2%  ;  $300. 

Page  401 

8.  $25,000,000 ;  $18,750,000.  11.  4%  ;  $31,900. 

9.  8%  ;  $1000.  12.  $30,000  ;  $3750  ;  $3000. 
10.  9%  ;  $9000.  13.  $6,500,000  ;  $13,500,000. 

Page  402 
14.  $18,575  ;  $105,000  ;  $62,175. 

Page  403 

1.  $475,000.  3.  $312,812.50.  6.  $290,312.50. 

2.  $273,125.  4.  $200,937.50.  6.  $268,437.50. 

Page  404 

7.  $376,2.50.  9.  $.304,500.  11.  $349,.562.50.      13.  $340,812.50. 

8.  $458,937.50.       10.  $471,187.50.      12.  $493,062.50.      14.  $416,937.50. 

1.  $1000,  loss.  10.  $2812.50,  loss.  19.  $1125,  gain. 

2.  $1812.50,  gain.  11.  $1375,  gain.  20.  $11,625,  gain. 

3.  $5750,  loss.  12.  $1500,  gain.  21.  $1750,  gain. 

4.  $875,  gain.  13.  $2250,  gain.  22.  $3750,  gain. 

5.  $3625,  loss.  14.  $2750,  gain.  23.  $2375,  gain. 

6.  $1625,  gain.  15.  $250,  loss.  24.  $250,  loss. 

7.  $1000,  gain.  16.  $250,  gain.  26.  59^. 

8.  $3312.50,  gain.  17.  $875,  gain. 

9.  $1625,  gain.  18.  $5000,  gain. 


28  PRACTICAL  BUSINESS  ARITHMETIC 

Page  405 
26.  200.  27.  $8,689.06,  loss.  28.  $249,875. 

Page  411 

1.  $26,906.25.     3.  $83,646.25.  .  5.  $45,238.75. 

2.  $612.50.  4.  $253,750;  $5087.50;  June  1,  1925;  $22.50. 

Page  413 

1.  $10,822.22.  4.  $14,245.42.  7.  $6010.83. 

2.  $19,860.56.  6.  $6370.  8.  $9876.26 

3.  $3867.92.  6.  $12,640.  9.  $11,251.67. 

Page  416 

1.  $600,  gain.       2.  $812.50.        3.  $440.26,  gain.        4.  $6529.33,  gain. 

Page  417 

6.  $762.64.  6.  $482.67 ;  $25.  7.  $2956.25. 

Page  418 

1.  $4357.50.  2.  $207.50.  3.  $123.76,  gain  ;  1.1+ %. 

Page  419 

4.  $6482.81,  gain.       6.  $478.75.  8.  $345,  gain.       10.  $16,417.67. 
6.  $75,  loss.                  7.  $116,  loss.        9.  $284.38. 

Page  425 

1.  $4403.20.     3.  $599.80,'  20-yr.  endowment.    6.  $708.45.        7.  $2602. 

2.  $3324.  4.  $2267.13.  6.  $11,001.61. 

Page  427 

1.  G,  $12,220  ;  H,  $24,440  ;  3.  $9000,  share  of  each  son  ; 

I,  $6110.  $12,000,  share  of  each  daughter. 

2.  F,  $2280  ;  D,  $1140  ;  E,  $570.       4.  A,  $7000  ;  B,  $4200  ;  C,  $6300. 

Page  430 

1.  $1392.25,  net  gain  of  each;  $6392.25,  Boyd's  present  worth;  $6392.25, 
Allen's  present  worth.  2.  $3786.46. 

3.  $9765.68.  ^^^^  ^^"^ 

4.  $10,249,  O's  present  worth  ;  $9949,  P's  present  worth  ;  $10,199,  Q's 
present  worth. 

1.  $10,099.16,  A's  present  worth  ;  $8899.16,  B's  present  worth. 

RE 


3 

I's  present 


ANSWERS  29 

Page  432 

2.  |4750,  A's  net  gain  ;  $2750,  B's  net  gain. 

3.  $12,052.36,  C's  present , worth ;  $10,276.18,  D's  present  worth; 
$10,276.18,  E's  present  worth. 

4.  $7323.26,  F's  net  capital ;  $8323.26,  G's  net  capital. 

5.  $31,700,  J's  net  capital;  $14,250,  K's  net  capital ;  $2550,  L's  net 
capital. 

Page  433 

1.  $831.16,  A's  share  ;  $1246.74,  B's  share  ;  $2077.90,  C's  share. 
$1020.10,  D's  share  ;  $1326.13,  E's  share  ;  $1428.14,  F's  share. 
$3844.20,  G's  present  worth ;  $2562.80,  H's  present  worth ;  $1922.10, 
resent  worth. 

Page  434 

4.  $1308,  gain  on  merchandise  ;  $800,  Robinson's  |  of  net  gain  ;  $400, 
Bressee's  ^  of  net  gain ;  $4800,  present  worth  of  the  firm  ;  $3200,  Robin- 
son's present  worth  ;  $1600,  Bressee's  present  worth. 

Page  436 

1.  $17,209.50,  present  worth  of  the  firm  ;  $10,150,  Brown's  net  invest- 
ment ;  $4850,  Hart's  net  investment ;  $15,000,  net  investment  of  the 
firm  ;  $2209.50,  net  gain  of  the  firm  ;  $11,254.75,  Brown's  present  worth  ; 
$5954.75,  Hart's  present  worth. 

Page  437 

2.  $43,461.10,  total  resources;  $12,400,  total  liabilities;  $31,061.10, 
present  worth  of  the  firm ;  $12,060,  Burgess's  net  investment ;  $9940, 
Clapp's  net  investment;  $9061.10,  net  gain  of  the  firm;  $16,590.56, 
Burgess's  present  worth  ;  $14,470.55,  Clapp's  present  worth. 

3.  $15,100.55,  total  resources;  $3258.25,  total  liabilities;  $11,842.30, 
present  worth  of  the  firm ;  $10,219.75,  Linden's  net  investment ;  $6057.70, 
firm's  net  loss;  $7680.25,  Greene's  net  investment;  $17,900,  firm's  net 
investment ;  $7190.90,  Linden's  present  worth  ;  $4651.40,  Greene's  pres- 
ent worth. 

4.  $1044.04,  net  gain  of  each  ;  $42,551.33,  total  resources  ;  $12,028.25, 
total  liabilities  ;  $30,523.08,  present  worth  of  the  firm  ;  $15,560.99,  West- 
fall's  present  worth  ;  $14,962.09,  Manning's  present  worth. 

Page  439 

1.  $5345.08,  R's  present  worth  ;  $4364.92,  C's  present  worth. 

2.  $28,700,  E's  present  worth  ;  $22,190,  F's  present  worth. 

RE 


30  PRACTICAL  BUSINESS  ARITHMETIC 

Page  440 

1.  $43,586.12,  total  resources;  f8460,  total  liabilities;  |35,126.12,  pres- 
ent worth  of  the  firm  ;  |19,302.50,  Cutter's  net  investment ;  $17,447.50, 
Woodward's  net  investment ;  $1623.88,  net  loss  of  the  firm  ;  $18,490.56, 
Cutter's  present  worth  ;  $16,635.56,  Woodward's  present  worth. 

2.  $1194,  Curtis's  net  gain ;  $796,  Barton's  net  gain  ;.  $9490,  present 
worth  of  the  firm ;  $5694,  Curtis's  present  worth ;  $3796,  Barton's  present 
worth. 

Page  441 

3.  $11,000.88,  cost  of  sales ;  $2908.21,  Palmer's  ^  of  net  gain ;  $2908.21, 
Mills's  i  of  net  gain ;  $2908.20,  Newbury's  ^  of  net  gain ;  $78,874.62,  total 
resources;  $10,150,  total  liabilities;  $68,724.62,  present  worth  of  the  firm. 

Page  442 

4.  $19,220,  Smith's  present  worth  ;  $12,715,  Osgoodby's  present  worth. 

5.  $14,596.95,  net  gain  ;  $5865.65,  Congdon's  net  gain  ;  $4365.65, 
Robinson's  net  gain  ;  $4365.65,  Moulton's  net  gain  ;  $91,336.95,  total 
resources ;  $27,240,  total  liabilities ;  $64,096.95,  present  worth  of  the 
firm ;  $23,425.65,  Congdon's  present  worth ;  $24,575.65,  Robinson's 
present  worth ;  $16,095.65,  Moulton's  present  worth. 


Page  445 

1.  $3;  4  mo. 

;  $87. 

2.  $36. 

3.  $950. 

Page  446 
Page  447 

4.  $270. 

1.  $466.80. 

2.  $511.37. 

3.  $582.63. 

Page  448 
1.  $0,995+.      2.  $8;  $240.      3.  $3600,  gain ;  28.8%.      4.  $6200,  gain. 


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UNIVERSITY  OF  CALIFORNIA  LIBRARY 


